From the Wikipedia article at
Discussion: why Ajax is so important
"AJAX solves the problem of asynchronously processing varied resources in one Web page. In short, AJAX eliminates the processing overhead of enforced synchronizing of multiple resources in the same page. Because of AJAX, the Web has been decomposed from pages as resource units to portions of pages as resource units. Informally, we may also say that AJAX makes the Web evolve from a web of URLs to a web of URIs. Such an evolution makes the Web be very different from before.
Although GMail is not the first AJAX application, it is the first influential AJAX application at the global scale that demonstrates the power of AJAX. By the success of GMail, AJAX caught the mainstream attention. With the wide adoption of AJAX, the rise of Web 2.0 became unstoppable.
GMail is a phenomenal product. The use of AJAX makes GMail be an interactive platform. Unlike the traditional email services such as Hotmail or Yahoo Mail (the versions before GMail), GMail let users feel that they are performing a regular desktop functions since the page refreshing issue has been nearly eliminated. Therefore, the first time in history two email users feel that they are using a shared desktop and interactively messaging each other. GMail becomes a platform for emails users more than simple an email service. This fundamental upgrade to the intent of email makes GMail immediately be popular among the Web users, let it alone the significant larger storage spaces GMail promised for its users." (http://yihongs-research.blogspot.com/2008/08/age-of-google-3-web-20.html)