For the unknowing, what's this Ajax thing? I myself look at it this way: until now all the action in your web-application has taken place at the server-side. The user's browser was only used for the view, to show the pretty charts, forms and reports. What's the main problem with web-applications today? They're unresponsive and don't feel as rich as normal Windows (or Mac OS X, Linux etc.) applications. The solution? Move as much to the browser as possible. Only contact the server if it's necessary. This not only makes your web-application more responsive, but also takes a lot of load from the server.
Does this actually work? Absolutely. Success stories are coming mainly from Google, which has become an expert on this technique, they include "Gmail":http://www.gmail.com and "Google Maps":http://maps.google.com.
If you search Google for "Ajax" right now, you'll mainly find hits about the popular Dutch soccer club, but that will soon change.