It's a publishing company.
From their website:
Chillingo is a leading Independent Games Publisher and a division of Electronic Arts. The company publishes innovative games and software for various platforms.
They don't develop games. Developers come to them and make various arrangements for their games to be published/distributed. It works in a similar way to how games for PC and consoles are produced: for example, Deus Ex: Human Revolution is developed by Square Enix, but published by Eidos Interactive.
Game publishers perform a variety of functions. They are generally responsible for marketing and production costs which might include the development of the games they publish.