When you make an account on one server, it doesn't duplicate that account to other servers. Each server is independent, but they can interact together.

It's like if you opened up a reddit thread while logged into your hacker news account, and decided to respond to a comment in the reddit thread. Federation would give you that ability. Your username, in that thread, would be something like "[email protected]" or something like that, to show that you were posting from a different server.