This was generally done to make web pages seem more like desktop applications.
Today the meaning of the term AJAX has broadened. Today the term AJAX is commonly used to refer to any web development technique that makes a web page dynamic. And not just techniques centered on the use of XMLHttpRequest to prevent page reloads.
Today AJAX is a synonym for DHTML.
However, it should be noted that very early on when the AJAX paradigm was coined, people started pushing using XMLHttpRequest with more than just XML. One format that gained popularity and is now closely associated with AJAX is: JSON.
As time went on, after the coining of the term "AJAX", people started developing libraries that made use of the AJAX technique. Many of these libraries started to include components that also did things that weren't strictly AJAX, but were DHTML instead.
Because of this, and because the generation of web developers who help give rise to AJAX were not familiar with the term "DHTML", the term "AJAX" was broadened to include all of what was traditionally called DHTML.
Other Things Named "Ajax"
Note that there are other things named "Ajax". Growing up, thre were a number of cleaning products called "Ajax". Some of the products I remember, are: Laundry Detergent and Dishwashing Liquid. There is no relation between the Ajax cleaning products, and the AJAX Web Development paradigm.