(oversimplified) they are "interconnected" just like emails are interconnected. I can log into Gmail and send an email to someone else at Hotmail. But I can't actually use Gmail credentials to log into Hotmail.

In the 'verse, "Federation" means every instance (I'm on aussie.zone) holds a copy of every other instance (I can see your post without ever visiting lemm.ee). This reply I'm posting is held in my instance, and a copy is sent to yours (and the whole Federation will also hold a copy and be able to see my comment).

If lemm.ee shuts down tomorrow, this conversation we're having will remain to exist in the thousands of other instances that are federated with lemm.ee today.

They are separate websites. They send copies back and forth. On Lemm.ee you're supposed to view Lemm.ee's copy of the Hexbear community on the Lemm.ee instance. Not head over to Hexbear.

Try searching for the Hexbear's Community URL through Lemm.ee and it will ask for a copy if it's not already on Lemm.ee.