Bucky Roberts of the New Boston gives the best explaination of AJAX out there on the web. "see video here"
AJAX allows you to update parts of a web page and not the entire page. It makes pages sleeker and faster and gives more of an interactive feeling to the page
It also allows for communication through XML and JSON's to the server to quickly update information in specified fields
AJAX gives partiality to a page and enhances the communication aspects through Asynchronous communication