A few days ago at HighRankings there was a thread asking about AJAX's use to develop websites. I chimed in with my $0.02 only to find that many folks in SEO are, apparently, unfamiliar with the new technology. From my post at HR:

AJAX means Asynchronous Javascript And XML - it's a way to use the web as a platform to serve applications in the same way that programs work in Windows or Mac OS.

It's a hot item right now because lots of developers, programmers and web users are excited about the possibilities of what can be done with AJAX as opposed to just web pages that submit information to a backend script for processing and return data. The idea is that all that can now happen on a single page (and that greater functionality and flow can follow from that).

I also really liked what linux_lover had to say about it:

I have developed a couple of apps with AJAX, and thats what they are 'applications' on the web.
I would not use AJAX to make a whole site with as it requires Javascript to work (and some SE's dont parse JS AFAIK).

I see AJAX in a similar way that I see Flash - as a nice way to incorporate bespoke interactions that you dont mind if the SE's dont see.

I see it as a great way to get some link love and some attention from the webdev community (who's currently fixated on the technology). It's very similar to what you can do with Flash actionscripting but it doesn't require the plug-in (although you can't have any JS blocking on).

I dug up a good site today that should help educate about AJAX through illustration - Max Kiesler's DesignDemo - which shows off (in Flash video, ironically) how AJAX elements provide superlative UI experiences. He's got samples from all over the web, including screenshots. If you're curious about what AJAX can do, it's not a bad place to start. You'll probably recognize that some of your favorite apps already use it - Google Suggest, GMail, and soon... SEOmoz!