Ubi is a multi-player game, which means it needs some way of identifying, uniquely, the person playing. The role of Facebook -- its only role -- is to provide those unique user IDs. That seemed easier than making the user create and remember yet another ID and password. The only hitch is, you need an account on Facebook.
We don't do anything else here with your Facebook credentials -- no digging through your hometowns, your likes, your list of friends. Possibly confusingly, you will see mentions of "friends" here, but those are not your Facebook friends. We have our own notion of friendship here: an Ubi friend is someone with whom you've shared a game map. (And to know what that's about, please log in with Facebook and press the "Help" button on the page that then comes up.)