The app identifies public Foursquare checkins from female (or male) users and then lets you look at her (or his) Facebook profile and photos.
This is all done with information Foursquare and Facebook users choose to share publicly. But the real uproar is over how easy it was for the developers of Girls Around Me to aggregate all that data into one super creepy app.
Since both Foursquare and Facebook have open APIs that let developers pull publicly-shared photos and checkins, it doesn't take a lot of imagination for a developer to come up with a way to broadcast all that data in a way the individual never intended it to be shared.
Girls Around Me is still live in the App Store, but luckily Foursquare has blocked its API from the app, rendering it completely useless.