The question is asked time and time again, and not always clear even to those who are working with Ajax!
The term Ajax is short for Asynchronous JavaScript and XML. It was coined in 2005 by Jesse James Garrett. Ajax is not a specific programming language or technology. Ajax is a Web development technique. Ajax brings dynamic data interactivity to Web pages. For example, a Web client sorts a column of data, and the data is automatically changed with live server data without reloading the entire page.
The appeal of Ajax is obvious – less waiting for the Web user and a more pleasant and responsive environment. This technique was seen before in other forms such as Microsoft’s Remote Scripting.
Ajax utilizes several different technologies to interact and exchange data with a server in a manner that is transparent to the client. A developer will implement a combination of HTML/XHTML and CSS for presentation, a client-side scripting language like JavaScript, and a data exchange method (usually the XMLHttpRequest object, but alternatively an IFRAME or dynamic script updates). The most common data format is XML, but HTML, plain text, and other formats are usable.

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[...] Any developer who has tangled with a Web app demanding lot of interface flexibility and options has had the added challenge of presenting an advanced interface in an intuitive fashion. User behavior can be hard to predict, but the Internet has been evolving long enough to identify a lot of habits that we as interface designers can draw from. New technology and development techniques make it easier to build a slick user experience, but we can also argue that as development evolves along with increased user sophistication we are just scaling up our pot of stew. [...]
[...] A word of caution implementing Ajax methodology in your apps. While the benefits are numerous, it’s important to make sure the app still works without XMLHttpRequest support unless you have a well-defined target user or platform. It’s also clear that the transition from traditional Web sites to robust Web 2.0 scripts can be system shock for your average user. It’s exceedingly important with all the new technology out there to meter the impact of the new technologies you implement and never add something just for the sake of adding it. [...]