Traditional Web Applications tend to follow the pattern that is described in the figure below, the first page is loaded when the user performs some actions such as filling a form or clicking a link. The user activity is then submitted to a server side program for processing while the user waits until finally a result is sent back to the user, which reloads the entire web page.
The problem with this model is that it is slow as it retransmits the entire data of the web page over and over in order to display the webpage with the results. Ajax web applications use a different model where user actions trigger behind the scenes communication to the server fetching just the data needed to update the page in response to the submitted actions. This process happens asynchronously, allowing the user to perform other actions within the browser while data is returned. The only relevant portions of the web page are refreshed.
The video below describes the Introductions to Ajax in detail.