Ajax is a way of developing Web applications that combines:
XHTML and CSS standards based presentation Interaction with the page through the DOM Data interchange with XML and XSLT Asynchronous data retrieval with XMLHttpRequest JavaScript to tie it all together
In the traditional Web application, the interaction between the customer and the server goes like this:
Customer accesses Web application Server processes request and sends data to the browser while the customer waits Customer clicks on a link or interacts with the application Server processes request and sends data back to the browser while the customer waits   etc....

Asynchronous
This is the key. In standard Web applications, the interaction between the customer and the server is synchronous. This means that one has to happen after the other. If a customer clicks a link, the request is sent to the server, which then sends the results back.

With Ajax, the JavaScript that is loaded when the page loads handles most of the basic tasks such as data validation and manipulation, as well as display rendering the Ajax engine handles without a trip to the server. At the same time that it is making display changes for the customer, it is sending data back and forth to the server. But the data transfer is not dependent upon actions of the customer.

When javascript was released, people loved all the cool things you could do with the web browser to make a more user-friendly experience. You could do form validation, quirky popup messages, make cool web tools and more. However, Javascript had no way of sending information between the web browser and the web server.

Example of AJAX Web Development is website that provides live update such as a stock exchange site. Where entire page is not reloaded but only section where you can see current market position keeps on constantly updating itself.

Ajax helps you in making your web application more interactive by retrieving small amount of data from web server and then showing it on your application. You can do all these things without refreshing your page. If you wanted to get any information from a database on the server, or send user information to a server-side script like PHP, you had to make an HTML form to GET or POST data to the server. The user would then have to click "Submit", wait for the server to respond, then a new page would load with the results. I'm sure we have all gotten slightly annoyed when having to wait for especially slow websites!

Usually in all the web applications, the user enters the data into the form and then clicks on the submit button to submit the request to the server. Server processes the request and returns the view in new page (by reloading the whole page). This process is inefficient, time consuming, and a little frustrating for you user if the only the small amount of data exchange is required. For example in an user registration form, this can be frustrating thing for the user, as whole page is reloaded only to check the availability of the user name. Ajax will help in making your application more interactive. With the help of Ajax you can tune your application to check the availability of the user name without refreshing the whole page.

Understanding the technology behind Ajax
Ajax is not a single technology, but it is a combination of many technologies. These technologies are supported by modern web browsers. Following are techniques used in the Ajax applications.