The Power Law refers to the unequal distribution of influence within networks.
"In systems where many people are free to choose between many options, a small subset of the whole will get a disproportionate amount of traffic (or attention, or income), even if no members of the system actively work towards such an outcome. The very act of choosing, spread widely enough and freely enough, creates a power law distribution." 
Commentary by Clay Shirky
Classic discusion of how the power law operates in blogs, and why it is inevitable, by one of the most influential commentators, by Clay Shirky.
"A persistent theme among people writing about the social aspects of weblogging is to note (and usually lament) the rise of an A-list, a small set of webloggers who account for a majority of the traffic in the weblog world. This complaint follows a common pattern we've seen with MUDs, BBSes, and online communities like Echo and the WELL. A new social system starts, and seems delightfully free of the elitism and cliquishness of the existing systems. Then, as the new system grows, problems of scale set in. Not everyone can participate in every conversation. Not everyone gets to be heard. Some core group seems more connected than the rest of us, and so on.
Prior to recent theoretical work on social networks, the usual explanations invoked individual behaviors: some members of the community had sold out, the spirit of the early days was being diluted by the newcomers, et cetera. We now know that these explanations are wrong, or at least beside the point. What matters is this: Diversity plus freedom of choice creates inequality, and the greater the diversity, the more extreme the inequality."
Critique of the 'naturalism' of the concept
A critique by Stephen Dowes at http://www.downes.ca/cgi-bin/page.cgi?post=33034
"Power Laws and Inequalities
Much of the work in networks has been on what are called 'scale-free' networks. A scale-free network is (as people like Barabasi have shown) distinct from a random network in that some entities in the network have a much higher degree of connectedness than others. True, in a random network, there will be a certain variance in distribution, but in a scale free network this variance is extreme. Consider, for example, a network like the internet, where some sites, such as Google, have millions of visitors, while other sites have only one or even none.
A scale-free network of this sort forms through a dynamic process where the presence of one entity leads others to connect to it. For example, consider the act of creating links on a web page. In order to create a useful link, it is necessary to connect to a site that already exists. This means that, all other things being equal, a site that was created first will obtain the most links, because it will have been a candidate for linkage for all subsequent websites, while a site that was created last will have the fewest links, because it has never been a candidate for links.
This effect can be magnified when preferential attraction is considered. For when creating a link on a web page, a designer wants not merely to link to a random page, but to a good page. But how does one judge what counts as a good page? One way is to look at what other people are linking to. The probability that the first page created will be found is greater than that for any other page, which means that the first page will obtain even more links that it would receive through random chance. With this and similar drivers, some websites obtain millions more links than others.
What's interesting is that though a similar process leads to the formation of scale-free networks in other areas, not in all cases is such an extreme inequality reached. What happens is that in some cases a structural upper limit is reached. Consider, as Barabasi does, the cases of airports and the power grid. Both are developed according to similar principles (airlines want to land flights, for example, where other airlines land flights). And, not unexpectedly, a power-law distribution occurs. But there is an upper limit to the number of aircraft that can land in a single airport, and consequently, a limit to the size of the inequality that can occur.
Various writers (for example Shirkey) write and speak as though the power law were an artifact of nature, something that develops of its own accord. And because it is natural, and because such systems produce knowledge (we will return to this point), it is argued that it would be a mistake to interfere with the network structure. This argument is remarkably similar to the argument posed by the beneficiaries of a similar inequality in financial markets. The rich get richer, benefiting from an inequal allocation of resources, but efforts to change this constitute 'intereference' in a 'natural phenomenon', the invisible hand of the marketplace, intelligently allocating resources and determining priorities.
This may be true, if we think of networks as natural systems. But the absence of limits to the growth in the connectivity of some nodes should alert us that there is something else going on as well. And it is this: the networks we describe, and in some cases build (or through legislation, protect), are interpretations of the multifarious connections that exist in an environment or in a society. They depend, essentially, on a point of view. And, arguably, the inequalities of links on the web or money in society represent the prevalance of one point of view, or some points of view, over others. But to understand how this could be so, we need to look at networks, not as physical systems, but as semantical constructs, where the organization of links is determined as much by similarity and salience than by raw, epistemologically neutral, forces of nature." (http://www.downes.ca/cgi-bin/page.cgi?post=33034)
Michel Bauwens discusses the power law in chapter five of the online manuscript on peer to peer, at