The name is shorthand for Asynchronous JavaScript + XML, and it represents a fundamental shift in what's possible on the Web.
Ajax isn't a technology. It's really several technologies, each flourishing in its own right, coming together in powerful new ways.
If the traditional web was letter writing, Ajax is instant messaging.
Ajax is a way of communicating with the server without refreshing the whole page.
You can update part of a document instead of refreshing the whole thing.
What's the big deal?
You can update part of a document instead of refreshing the whole thing!
Holy crap!
Communication with the server is what distinguishes Ajax from DOM Scripting/DHTML