ASP.NET AJAX is released by Microsoft for quickly creating efficient and interactive web applications that work across all popular browsers. ASP.NET AJAX includes both client side and server side components which allows the developer to create web applications in ASP.NET that update data on the web page without posting page back to server. Desktop applications are usually very fast because they are running on your computer. You are not waiting an internet connection. That is why they provide quick user response.On the other hand web applications provide services that you could never get on your desktop. However , with the power of web waiting for server respond, a screen to refresh, and request to come back and generate a new page. The keyword AJAX(Asynchronous Javascript using XML) defines a development framework which aims to improve web page usability . This technique is basically evolved to shift the work load from server side to client side. Adavantage of using AJAX 1) Aimed at improving user experience with web pages. 2) Make multiple AJAX calls with different request from the same page. 3) Instant result. 4) Not to wait for the page to get reload. 5) Makes web processing responsive and timesaving. 6) It supports every modern browsers.Hope that it will helpful for readers.Thanks & Regards Farukh

Here is the answer. This article talks exactly about why we should use AJAX in our applications. 

Getting Started with AJAX 1.0 by Mahesh Chand on Apr 06, 2007
After fruition of this article, you will have a better understanding of AJAX 1.0 extensions and will learn how to build AJAX enabled Web applications using ASP.NET 2.0 and Visual Studio 2005.