The basic premise is very close to Dodgeball, in that the system basically revolves around "checking in" -- whenever you go out to a bar, you hit a button in the app that says something like "Hey, I'm at Tin Lizzie," and then everyone in your friends list (and your Twitter followers, if you have that option set) sees where you are.
In addition, however, they've added some new features into the mix: you get "scored" on how many times you go out and when you go out to different places. And there are even "achievements" you can earn (eventually user created) for trying a hot dog at everyone's favorite stand, or drinking x number of beers at a popular bar. In fact, there's even awards for going to bars where less-than-fashionable people appear, so watch where you decide to spend your Saturday night, lest you pick up the d-bag award.
As you might have surmised, it's an app for the barhopping crowd; in fact, that's kind of what kept Dodgeball from getting any bigger than it did: it was mostly confined to a group of New Yorkers who knew the trendiest places to go, and wanted to know when their friends were there. But Foursquare has potential, as the folks in Austin are discovering this week. In addition to the "join your friends" idea, it works well as a tour guide (where are the most popular places around you right now?), and can even help to get yourself out of the house (visit a certain bar enough times and you can get recognized as the "mayor" of that establishment). It's only available in 12 US cities right now, but don't forget that SXSW was also the breeding ground for Twitter -- we'll have to see if Foursquare languishes like Dodgeball or takes off like the tweeting bluebird.