A few things:

1) It makes user management stupid-simple. I can authenticate with Facebook/Twitter/signup easily (not that it's really that hard, but still), and the user info is automatically saved to the cloud.

2) I then use it to store game state, retrieve a list of active games/previous games.

3) Push notifications are really easy. Each client opens a "channel", and the other client sends a push to their opponent's channel after their turn is complete.

I suppose I should clarify that I am building a turn-based iPad game, where the game state needs to be stored between turns.