Ahh... Ajax.
Ajax is a relatively-recent programming model for web applications. The name is shorthand for Asynchronous JavaScript + XML, a phrase coined by Jesse James Garrett of Adaptive Path.
As defined by Garrett, Ajax is actually a combination of several well known technologies:
To cut a long story short, Ajax is usually used to enable changes in web pages to happen dynamically, without a full page refresh. From the user point of view, this provides an experience that is closer in model and performance to that of an interactive desktop application.
There are plenty of articles about Ajax, but I would start from this two:
Note that Ajax is often stated as a requirement for a web application to be considered as part of the "Web 2.0" wave. Even worse, Ajax is sometimes considered as what makes an application "Web 2.0". Oh well...