Connecting a profile to Facebook is used to save your profile information, score, and leaderboard rank for online mode. This way, they remain intact after reinstalling the app or transferring the account to another device.
If you would like to delete an app that is connected to Facebook to get a new account, don't forget to disconnect your old account from Facebook. This is the only way to connect it to your new account.
Exception: In Checkers the connection to Facebook is required directly for login and therefore must not be deactivated.