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.
When you turn federation off, your users can only see activity and posts from your own instance.
Federation is what enable you to seamlessly interact with all the other instances. This can also be set at yhe instance level, to pick and choose which other instances your instance can talk to.
Federation is the process that pulls content in from other servers (e.g. lemmy.world, beehaw.org, fedia.io, mastodon.social, etc.) All of these different servers can communicate and share content with each other.
If you turn federation off, you only see content from your "home" server, which in your case is kbin.social (in mine it's remy.city).
As I understand it, it's a bit like email in that there is a protocol to allow different servers/websites to communicate, allowing the user to access the whole collection of Lemmies but meaning there is not one corporation or person in charge of the Lemmiverse.
This has advantages in that someone can't pull a Spez, but disadvantages in that it can make stopping bad actors from affecting other instances.
Someone else will probably make a clearer explanation, and I'm happy to be corrected on any of this.
There is also Kbin (that I use) which can communicate with Lemmy. Since they both share the "sections/communities/groups with threads in them" concept, they can interact pretty well.
I've seen folks calling it the "Threadiverse" because of the different software that servers run.
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