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http://www.w3schools.com/Ajax/Default.Asp
that is a good place to start. This should answer all of your questions.
Creative use of previously known technology. Both the browser side scripting and programmatic access to data on the server have been known before. In AJAX it has been put together for innovative use anabling new applications of thechology known before. The REST comes to mind as similar type of advance...
AJAX is very simple : someone somewhere tought that it would be cool to be able to send something to the server and receive something from it without reload a page.
AJAX is not a revolution, it's just a name for something simple : a web page can send a request to the server without being reloader - just some asynch stuff here.
You can add AJAX controls on your web pages wihout any works - just drag them in with Visual Studio. You may have to add some manager for them, but it is simply a drag-and-drop task.
But be warned : rogue web browser usually don't speak the same AJAX language as IE...
:)