Like most services, Foursquare has long had a developer API that allows users to plug Foursquare data into other apps. Now that idea is evolving with Foursquare's new Connected App Platform. With Connected Apps, developers can build their app or service into Foursquare - essentially, apps will run within Foursquare to enable new kinds of user experiences.
Ignore that those are iOS screens - the service will be cross-platform. The new APIs are just a developer preview right now, but already Foursquare has worked with its various partners to get the ball rolling. Apps like Eat This Not That, GroupMe, and Untappd have all built Connected App experiences.