Here's the techy bit:
http://en.wikipedia.org/wiki/AJAX

How it's used:
Ajax is a Javascript platform (or in my opinion a 'methodology') that enables the application and server to exchange 'small' amounts of data after a page has loaded.

For example, I'm replying to your post with the quick reply feature on Webforumz. Ajax is used to send the post (along with any other relevant information). The response of the ajax call is used to display my brand new reply within the thread as it would if I had refreshed the page, but I didn't have to. Rather than reloading the entire page, Ajax is used to update a small section of the page with some new data...

That's just one use, the posibilites are endless.
Google Maps is my favourite...