Loosely speaking, Foursquare has always been a sort of social network, but the company is looking to get a lot more social with their new app. Instead of focusing on the relationship between businesses and customers, Swarm is all about you and your friends. Everything contained within is focused on getting groups together.... though if you did so at a local bar or cafe, Foursquare probably wouldn't mind.
There are three components to Swarm: a Facebook/Twitter-style news feed, a standard messaging system, and a social map. The former is pretty obvious, showing events and short posts from your friends, which can include other tagged users. This is a more functional version of Foursquare's existing social integration. The messaging system is pretty self-explanatory, though there's a focus on geolocation and the like. The social map will show you friends who are nearby, and if possible, what they're doing. That's the hook for you to go hang out without prompting, and/or to crash someone's bar crawl.
Foursquare's central check-in system is retained, and the app is pretty enough, with a clear layout and bright colors. Still, it's hard to see how useful this is unless your social circle is constantly within a mile or so of each other (college students, this is probably right up your alley). If your buddies are more spread out, or you live in a more sprawling city, I imagine existing SMS and social networks are still a better option for you.
Swarm is free for Android Gingerbread and up, and there's an iOS client available as well.