The name AJAX is an acronym for Asynchronous JavaScript and XML.
AJAX isn’t a single programming language, but rather a collection of state of the art technologies such as HTML, DHTML, DOM and JavaScript.  This give AJAX a huge range of functionality and makes it easy to learn and familiar to most webmasters. 

AJAX can be used for Desktop as well as Web applications.  The key advantage of  AJAX for either Desktop or Web applications is the ability to continuously update information.  With static programming languages, users must perform some action, such as pressing a Submit button, to update the displayed information.   With AJAX, the information displayed is continuously updated.

In a typical web page that uses CGI or PHP, a web page is loaded into the browser and the information is ‘fixed’ until the browser ‘does something.’  This is called the submit/wait/redisplay paradigm.  To change the information displayed in the browser, visitors to your website have to press a submit button, wait for the server to process the information, then reload the page.   A good example is online games.  Most online games require a plug-in or a download.   This requires a complicated sequence of steps for browsers, in addition to a basic level of computer and Internet knowledge.  If your visitors do not complete this sequence or are unable to complete it, you will lose visitors.   AJAX games play directly in any JAVASCRIPT enabled browsers without plug-ins or downloads.

Another example is popular shopping carts.   With AJAX, the total number of products and total dollar purchase amount are updated dynamically.  This eliminates users having to press an update button, wait for the server to re-calculate their total and reload the page.

The benefits for e-business owners:

• Increased Usability.    Browsers get what they want faster and with fewer clicks and with less waiting.  If your site is easier to use, browsers come back.
• Reduced Bandwidth.   AJAX updates only parts of a webpage, not the whole page resulting in significant savings in bandwidth. 
• Increased Conversion.   Browsers can access information faster and with fewer clicks.  The more browsers have to click to find what they want, the less likely they are to buy.  
• Better overall experience for browsers.   Basically browsers are lazy and impatient.  They are also in total control with the BACK button one click away.  Browsers will return to and buy from websites that are easy to use and give them exactly what they want as quickly and easily as possible. 
• Cross Platform.   AJAX applications run on any platform including MACs, PCs, or cell phones, including Apple’s new iphone.