In very simple words, Ajax is a set of technologies, which allow Asynchronous loading of content in the browser window of end user. When the user does some modisications on the webpage, the page need not be reloaded from server to reflect the changes.
Main benefits of Ajax are increased interactivity and increased user experience.
The word was coined in Feb 2005! By Jesse Garrett to describe the technologies for asynchronous loading.
Here are some figures to explain Ajax: