Federated identity manages user data across multiple networks, and denotes where the credentials are stored. Your "federal" system becomes an "identity provider." When a user logs into your website, instead of providing credentials to Muut, we trust the "identity provider" to validate those credentials. So the user never has to log into Muut, and never provides us with information.
You could, for example, tie your WordPress user accounts into Muut. It would then allow users to login and signup with your own WordPress authentication system. Once logged in, they'll be able to use Muut commenting and forums without having to create or login to an account through Muut.
This creates a seamless integration between your own website's user authentication and your Muut community solution.