From a post on the foursquare Blog:
foursquare was created with a core set of 16 badges, designed to reward and motivate all of you. As we’ve grown, we’ve tried to expand those offerings to make foursquare fun for everyone, from the Dog’s Best Friend to the Great Outdoors, to partnerships with applications like RunKeeper and organizations like The Wall Street Journal. Starting today, there’s a new Trophy Case to house all these badges, and a Partner Badge program to create even more.
In the Trophy Case, you’ll also get a clearer picture of how many badges you’ve unlocked, and which of your friends have unlocked each of them.
The Partner Badge program is still in its early stage, and we’re slowly expanding it. If you are an organization that would like to create a badge, fill out this form.