Emergence = there are emergent layers of complexity in nature, but also that different qualities arise with each new layer.
“Emergence is when the output of a system is greater than the sum of its components. Emergence is the duplication low-level order on a higher systemic level.” (Johnson 2001 p. 26) 
Timothy Burke :
The basic core of the idea, that emergence is defined by the formation of complex patterns or systems from simple initial conditions without any governing or controlling blueprint or design
From the Wikipedia at http://en.wikipedia.org/wiki/Emergence:
"the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems."
And some common characteristics:
(1) radical novelty (features not previously observed in systems);
(2) coherence or correlation (meaning integrated wholes that maintain themselves over some period of time);
(3) A global or macro "level" (i.e. there is some property of "wholeness");
(4) it is the product of a dynamical process (it evolves); and
(5) it is "ostensive" - it can be perceived." (http://en.wikipedia.org/wiki/Emergence)
Science writer Fritjof Capra describes them:
"At each level of complexity the observed phenomena exhibit properties that do not exist at the lower level. For example, the concept of temperature, which is central to thermodynamics, is meaningless at the level of individual atoms, where the laws of quantum theory operate. Similarly, the taste of sugar is not present in the carbon, hydrogen, and oxygen atoms that constitute its components…According to the systems view, the essential properties of an organism or living system are properties of the whole, which none of the parts have. They arise from the interactions and relationships among the parts. These properties are destroyed when the system is dissected." (http://www.pulsethebook.com/the-new-biology/19-emergence/)
Cited by Ming the Mechanic at http://ming.tv/flemming2.php/__show_article/_a000010-001883.htm
"Clustering would be where a bunch of somethings get together and do the same thing. Like slime mold. Or a flash mob, or other group phenomena where large numbers of people suddenly get excited about one thing or another, and they all show up at the same time, or they do the same thing.
Coping would be where a bunch of individuals get together, and they don't just do one simple thing, but they form a more complex organization. Like an ant hill. The ants specialize, they take on different roles, they solve problems, they change their behavior if necessary, etc. Without anybody handing out the orders.
It is a lot easier to simply get a large number of people together, or to get them together for one well-defined purpose, than it is to get large numbers of people to self-organize towards solving unknown problems.
Somebody suggested the Howard Dean presidential campaign as an example of a bottom-up emergence of the clustering kind. It was a successful attempt of getting a lot of people together in being excited about one thing, organizing their own local meetings to futher it, etc. But it only worked as long as the main point was being excited about Dean being a leading candidate, and as long as things went well. The moment people started being dissatisfied about something, or they wanted to change direction, there was no vehicle for that, and it fell apart rather quickly. It wasn't the Coping kind of emergence. I don't think it really was emergence at all. That a political candidate gets a lot of grass-roots support might be interesting, but it isn't something that emerged from the grass-roots, or it would have been the assembled crowds that told him what to say, rather than him telling them what to be excited about." (http://ming.tv/flemming2.php/__show_article/_a000010-001883.htm)
From an essay by Margaret Wheatley and Deborah Frieze, entitled Using Emergence to Take Social Innovation to Scale, reposted here at http://www.evolutionarynexus.org/node/620
What is Emergence?
Emergence violates so many of our Western assumptions of how change happens that it often takes quite a while to understand it. In nature, change never happens as a result of top-down, pre-conceived strategic plans, or from the mandate of any single individual or boss. Change begins as local actions spring up simultaneously in many different areas. If these changes remain disconnected, nothing happens beyond each locale. However, when they become connected, local actions can emerge as a powerful system with influence at a more global or comprehensive level. (Global here means a larger scale, not necessarily the entire planet.)
These powerful emergent phenomena appear suddenly and surprisingly. Think about how the Berlin Wall suddenly came down, how the Soviet Union ended, how corporate power quickly came to dominate globally. In each case, there were many local actions and decisions, most of which were invisible and unknown to each other, and none of which was powerful enough by itself to create change. But when these local changes coalesced, new power emerged. What could not be accomplished by diplomacy, politics, protests, or strategy suddenly happened. And when each materialized, most were surprised. Emergent phenomena always have these characteristics: They exert much more power than the sum of their parts; they always possess new capacities different than the local actions that engendered them; they always surprise us by their appearance.
It is important to note that emergence always results in a powerful system that has many more capacities than could ever be predicted by analyzing the individual parts. We see this in the behavior of hive insects such as bees and termites. Individual ants possess none of the intelligence or skills that are in the hive. No matter how intently scientists study the behavior of individual ants, they can never see the behavior of the hive. Yet once the hive forms, each ant acts with the intelligence and skillfulness of the whole. And over time, even though the individual ants die off, the hive develops greater intelligence.
This aspect of emergence has profound implications for social entrepreneurs. Instead of developing them individually as leaders and skillful practitioners, we would do better to connect them to like-minded others and create the conditions for emergence. The skills and capacities needed by them will be found in the system that emerges, not in better training programs.
Because emergence only happens through connections, Berkana has developed a four stage model that catalyzes connections as the means to achieve global level change. Our philosophy is to “Act locally, connect regionally, learn globally.” We focus on discovering pioneering efforts and naming them as such. We then connect these efforts to other similar work globally. We nourish this network in many ways, but most essentially through creating opportunities for learning and sharing of experiences and shifting into communities of practice. We also illuminate the work of these pioneering efforts so that many more people will learn from them. We are attempting to work intentionally with emergence so that small, local efforts can become a global force for change." (http://www.evolutionarynexus.org/node/620)
The Life-Cycle of Emergence
Stage One: Networks.
"We live in a time when coalitions, alliances and networks are forming as the means to create societal change. There are ever more networks and now, networks of networks. These networks are essential for people finding likeminded others, the first stage in the life-cycle of emergence. It’s important to note that networks are only the beginning. They are based on self-interest--people usually network together for their own benefit and to develop their own work. Networks tend to have fluid membership; people move in and out of them based on how much they personally benefit from participating.
Stage Two: Communities of Practice.
Networks make it possible for people to find others engaged in similar work. The second stage of emergence is the development of communities of practice (CoPs). Many such smaller, individuated communities can spring from a robust network. CoPs are a self-organized. People share a common work and realize there is great benefit to being in relationship. They use this community to share what they know, to support one another, and to intentionally create new knowledge for their field of practice.
These CoPs differ from networks in significant ways. They are communities, which means that people make a commitment to be there for each other; they participate not only for their own needs, but to serve the needs of others.
In a community of practice, the focus extends beyond the needs of the group. There is an intentional commitment to advance the field of practice, and to share those discoveries with a wider audience. They make their resources and knowledge available to anyone, especially those doing related work.
The speed with which people learn and grow in a community of practice is noteworthy. Good ideas move rapidly amongst members. New knowledge and practices are implemented quickly. The speed at which knowledge development and exchange happens is crucial, because local regions and the world need this knowledge and wisdom now.
Stage Three: Systems of Influence.
The third stage in emergence can never be predicted. It is the sudden appearance of a system that has real power and influence. Pioneering efforts that hovered at the periphery suddenly become the norm. The practices developed by courageous communities become the accepted standard. People no longer hesitate about adopting these approaches and methods and they learn them easily. Policy and funding debates now include the perspectives and experiences of these pioneers. They become leaders in the field and are acknowledged as the wisdom keepers for their particular issue. And critics who said it could never be done suddenly become chief supporters (often saying they knew it all along.)
Emergence is the fundamental scientific explanation for how local changes can materialize as global systems of influence. As a change theory, it offers methods and practices to accomplish the systems-wide changes that are so needed at this time. As leaders and communities of concerned people, we need to intentionally work with emergence so that our efforts will result in a truly hopeful future. No matter what other change strategies we have learned or favored, emergence is the only way change really happens on this planet. And that is very good news." (http://www.evolutionarynexus.org/node/620)
Emergence in Artificial Societes and Virtual Worlds
Timothy Burke (excerpts from long article):
"“Emergence” is a difficult concept to grasp and employ. In some formulations, it comes close to being a truism, or so broad as to be virtually meaningless. In both artificial societies and virtual world research, however, the concept tends to be more specifically defined and used. The basic core of the idea, that emergence is defined by the formation of complex patterns or systems from simple initial conditions without any governing or controlling blueprint or design, is generally coupled with an interest specifically in cases of emergence that involve rule-driven agents that act independently and simultaneously within and upon an environment which is distinct from the agents.
For researchers working on artificial societies, the concept of emergence and related ideas is explicitly invoked and foundational to the distinction between artificial societies simulations and other kinds of social-science modeling. Emergence is taken both as a sign of the resemblance between artificial society simulations and the real world, and as a protection against tautological manipulation of the simulation. If a given simulation can produce complex behaviors or patterns from simple agent-based starting conditions, many artificial society researchers take that as a reasonable confirmation that real-world complexities of a similar kind have followed a similar process of evolutionary development.
In virtual worlds research, however, the use of the idea of emergence is much more implicit, rarely invoked in detail. Richard Bartle, for example, describes the content of virtual worlds that arises “from the natural actions of players” as “emergent or self-generating”, which he distinguishes from content explicitly or intentionally designed by either developers or players.  Nevertheless, many researchers and virtual world designers are conversant with the concept: at the Game Developers Conference in September 2004, developer Warren Spector based his keynote speech around the term, noting both its ability to incisively describe familiar patterns of gameplay and virtual world structure and its applied possibilities for solving long-standing problems of implementation and design.  In many cases, I would argue, developers and researchers interested in virtual worlds who make no explicit or deliberate use of the term or the body of research related to it nevertheless write in terms which recognizably invoke these concepts and ideas in some fashion.
Artificial society simulations encounter a number of issues in their bottom-up, emergence-driven approach. First, emergence-based artificial society simulations to date tend to have a lack of new outcomes traceable to later events in a system’s evolution. The end-state or later complexity of the simulation tends to directly derive from the initial condition. Most such simulations tend to settle into relatively stable self-organizing states which can only be stimulated to new development or change through user intervention. Yet if emergence applies to real human social or cultural evolution, then in this respect the simulations are very poor models indeed, as complex structures or patterns which arise from particular simple antecedents tend to generate in turn yet more patterns or novel structures, each as potentially unpredictable or surprising in their own way as the initial flowering of self-organizing patterns might have been. Moreover, there is at least some legitimate reason in the context of real human social dynamics and history to think that some of this “emergence from emergence” is contingent, that re-running the “tape of history” would not produce the same results, as Stephen Jay Gould memorably suggested in his book Wonderful Life. Agent-based “bottom-up” artificial society simulations have a limited ability to demonstrate similar contingency.
This leads to a second problem with emergence-based approaches in social simulation, that results or end-states can be very hard to quantify and rigorously describe. Emergent systems are quintessentially process-driven and dynamical in their form: you have to see them in motion in order to fully understand them. Seeing any single static representation of such a system, whether simulation or real-life example, tells you relatively little. Various graphings or representations of the dynamic evolution of such a simulation can provide usefully compressed information about their histories, and the artificial society approach does permit researchers to study non-equilibria dynamics in ways that other social science instruments find prohibitively difficult. To some extent, dealing with the first issue I noted makes this problem far worse. It is not that it is technically impossible to simulate emergence at multiple scales or levels, but that the more levels of emergent processes that an artificial society contains, the more difficult it is to make a meaningful connection between changes in the initial conditions of the simulation and its dynamic behavior over time, the more difficult it becomes to offer any rigorous or quantitative statement about what happened in a particular iteration of the simulation."
For virtual world researchers, the observation and analysis of emergent sociality within MMOGs and similar computer-mediated environments is the central substance of their work. Unlike artificial society researchers, virtual world scholars are not exploring hypotheses through a process of controlled simulation design. They are commenting on social dynamics which take place within relatively uncontrolled contexts. Yet like artificial society simulators, these researchers are dealing with a case of agent-based emergence that is tantalizingly comprehensible because of its relative simplicity in comparison with the real world. It is not merely that virtual worlds are defined and constrained by the code used to make them, but that real human beings within such environments are essentially turned into rule-based and relatively simplistic agents. Virtual worlds rest on the Turing Test in reverse, the truncation of the complexity of human individuals into manageably simple rule-constrained software-expressed agents.
Just as artificial society simulations in theory may permit a researcher to hypothesize a cause-and-effect relationship between some set of simple initial conditions and some complex pattern or system, virtual worlds allow scholars to argue that intricate patterns of social practices and institutionalized behavior evolving over time within those worlds derive from basic rules governing player actions within the game environment. Virtual worlds have a real initial condition, a moment where they are uninhabited by agents; they have histories which can be observed, recorded, traced. Concrete, specific changes are made to their rules and their environments whose propagating social effects can be observed and described.
There are now a great many specific examples of emergent dynamics known to researchers from MMOGs, MUDs and other virtual worlds. Andrew Leonard, for example, has described the cascade of social and environmental consequences from the introduction of a Barney the Purple Dinosaur bot into a text-based virtual world called Point MOOt in 1993 . Players who initiated violent action against Barney caused the bot to replicate; each Barney bot wandered freely throughout the virtual environment. It would not have been that hard to guess that this particular design feature (violence leading to replication) would lead to massive increases in the number of Barneys. This in turn led designers to add a new wrinkle to their economic model, which paid players in development resources for adding new elements to the world but also allowed players to go on a form of welfare. Barney-hunting became one of the welfare-work assignments players could receive. As Leonard observes, this in turn drew more player attention to the Barneys, and they discovered other ways to make them replicate even further (such as typing the command “feed”). The result: population growth outstripped the ability (or interest level) of any Barney-hunter to abate it." (http://weblogs.swarthmore.edu/burke/?page_id=31)