A typical ASP.NET web page contains buttons and links that perform socalled postbacks when clicked. That is, a request is sent back to the server and the whole page (or frame) is reloaded. It doesn't always look nice.
With AJAX the postback is performed in the background. For instance when a button is clicked it calls a script which in turn sends a request to the server. Upon response the script may choose to update only parts of the page (update an image or add a row to a table etc.). The result is a better experience for the user (no flashing or partially loaded pages and so on).
You can use ASP.NET to create AJAX enabled pages.