To try to clarify for you:

Imagine you could have your own entire reddit that you can install on a server and let other people join and use. On your reddit, they can create subreddits, make comments, make posts, and everything else you would expect.

Now imagine other people do the same thing. Many other people. They make their own reddits on their own servers which have their own subreddits, users, posts, comments, etc. Imagine I am one of these other people, and I have my own version of reddit on my own server.

Federation is where between you and I and everyone else, between all these peoples own personal reddits, posts and communities will show up from all of the reddits on everyones front page, and everyone can interact with them regardless of whose reddit they are actually on.

You might make a post on your own reddit, in a subreddit there called “mySubreddit”. Even though I am on my own server, I see this post you have made on the front page of my server, and I can comment on it, make posts on “mySubreddit”, upvote and downvote, everything you would expect.

This works both ways. I can make posts on the version of reddit running on your server, see its communities etc, and you can do the same on mine.

Now replace the word “subreddit” with “community”, the word “server” with “instance”, and the word “reddit” with “lemmy”, and this is how the platform works.

This means you can have a large group of people like reddit does, interacting with one another, but without any one person or a business having to buy and manage entire server farms, moderate an enormous platform, or any of the other major logistical stuff.

It means that no company owns it as well. Lemmy also can’t “go down” like reddit, because reddit is not federated. If reddits server has an issue, no one can access reddit. If lemmy.ml goes down, you can still see lemm.ee, lemmy.world, lemmy.one, or any of the other lemmy instances, because they are different entire servers owned by entirely different people that are managed and configured separately from one another.

Your account is on lemm.ee, which is an instance of lemmy on someones server. My account is on lemmy.ml, which is a different instance - someone elses server. And yet, we can hold this conversation because of federation. The community (subreddit) this conversation is taking place in is lemmy.ml/c/asklemmy, which is a community on my home server where my account is stored. Your account does not exist here, but you didnt have to create a lemmy.ml account to see this community, or the post, or my comments, or to reply to me, because federation allows your account to work on lemmy instances that are federated to your lemm.ee home server.

This also keeps you from getting banned from the entire platform over ridiculous things. At most, you can be banned from an entire Lemmy instance. This is good because if an instance has a change of ownership, and the new owner is an asshole, you can’t be locked out of the entire platform, you can always just create another account on a different lemmy instance without fear of being banned again (so long as you follow the respective rules on whatever instances you are communicating in). Furthermore, the mod logs are public data, and can be viewed from the sidebar of communities, so it is easy to see if a mod or admin is an asshole.

I’m glad to take any follow up questions or provide further clarifications.