Ajax is an acronym for
With Ajax, web applications can send data to, and retrieve data from, a server asynchronously (in the background) without interfering with the display and behavior of the existing page.
Ajax With WordPress
From the Codex:
the core of WordPress uses Ajax only in the administration screens. For instance, Ajax is used for instant updates when you are doing comment moderation, and when you are adding and deleting items from lists such as categories, blogroll, and posts; Ajax is also the technology behind the auto-save functionality on post and page editing screens. Several themes and plugins also use Ajax; for instance, some post rating plugins use Ajax to store the visitor's rating in the database and then display an updated average rating.