Related to this, google has released a toolbox framework http://code.google.com/webtoolkit/
One page thats good for showing off what it can do is here:
http://code.google.com/webtoolkit/documentation/examples/kitchensink/demo.html
Also, the tutorial here is a nice way to start:
http://www.w3schools.com/ajax/default.asp
Examples of where it can be used, at one stage there was a script on LW that refreshed your new PM's. It went back to the server every 1min and only had to load a tiny bit of HTML without refreshing the whole page. You do have to remember though that this is still a pull technology, not push so it can create high loads on servers when checking, hence why LW no longer uses this.
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Anyone who isn't confused really doesn't understand the situation
http://craigk.org/pictures/
Can you work out the code?