If Twitter asks "What are you doing?", foursquare asks, "Where are you and what's on your mind?"
The reason Twitter blew up a few years ago at SxSW is because everybody there joined it. Everybody was going to parties and tweeting where they were. Back then it was all new, but Twitter has evolved into something almost spammy, at least to the 1% of people in the bay area that live and breathe by it.
foursquare is different though. Instead of giving users the freedom to blurt out 140 characters of whatever their heart's desire, they are required to just name a place. Any extra info you want to include can be attached at the end.
In Austin this year, the foursquare app is very useful to see where everybody is all the time.
The thing that distinguishes this app from other location-based social networks like Brightkite and loopt is that there are merit badges you can earn for different accomplishments. For instance, you are mayor if you are the number one user of a certain place.
In Austin this year, there are 16 special badges you can earn for going to 16 different parties. Honestly, it makes the app more fun to use.
This is the famous photo of the founders of Dodgeball, the deceased Google geo-location property. They left Google to build foursquare, and I think they made the right move.
Lots of people are saying that this is the big hit of SxSW, and I agree. When you are sitting around in a bar and looking for your friends, just jump on foursquare and see where the party is. There is also something fun about checking into places. It's kind of like a location-based diary of where you've been.
The iPhone app is awesome too. I don't have one, so I can't show screenshots, but check out ReadWriteWeb's post.
Another great post is by MG at Venturebeat.