If you turn federation off you only see content from the server that you are on. For your case, this means content only from the kbin.social server. I’m on kbin.dk, so if I turn federation off I wont see any content from kbin.social, but only content from my own server where we currently only are a couple of users.

Federation (through the ActivityPub protocol) allows you to subscribe to content from other servers. If you, e.g., subscribe to the magazine @musik from my server, then kbin.social will create a local magazine and start receiving new content posted on my server.

Federation also allows me to comment on your post on kbin.social without using an account there. I am using (https://kbin.dk/u/cnk)[https://kbin.dk/u/cnk]. Since federation happens through a standardized protocol, you can also subscribe to content from servers running different ActivityPub software. The closest cousin is Lemmy that’s also a forum/link aggregator. But you can also communicate with, e.g., Mastodon that is a microblogging platform.