Simply defining, Asynchronous Javascript And XML (Ajax) is the method of making HTTP server requests using Javascript code, and
fetching the server response without reloading the web browser.
While almost all modern browsers have the inbuilt capability to handle Ajax applications, it only very recently that these applications have become popular. Google Maps, GMail, Zuggest, and AjaxPatterns Wiki Demo are some popular applications, which are based on Ajax.
Read more about Ajax, reasons behind its populariy, lifecycle of an Ajax application etc. at Ajaxpatterns.