To make it more understandable, it is a way to create an application that responds to the actions of the user without refreshing the page against the server.
HTML - it distributes the elements of the application and the information received by the server in the window of the browser.
CSS - It defines the aspect of each element and data of the application.
XML - it is the data's format transmitted from the server to the client (user) showed later.
Server language - It generates the useful information in XML and sends it to the browser.
An excellent example of AJAX application, quite compatible between browsers, isGoogle Maps, where you will be able to see how we change the map's position without reloading the page..