Let’s imagine there are 3 magic books, and what someone writes/draws/glues onto the pages of one of them appears in all 3 simultaneously. You can use them to share stories, articles, pictures, have conversations, etc. Those 3 books are federated.
If one of those books gets lost, stolen, damaged, etc. everything still exists in those other 2 books and they can keep talking to each other. and if/when the lost book is found or repaired, it will get backups of everything from the other 2 books.
Now let’s say the owner of books 1 and 3 have a falling out, and they break the spell federating their books together, but each of them remain federated with book 2.
Books 1 and 3 can no longer see what the other is writing in their book, but everything they already wrote is still there, and they can still see what 2 is doing, and for anyone using book 2 nothing much has changed, except that they no longer see 1 and 3 getting into arguments with each other in the pages.
The books are the different Lemmy instances, anything anything written, drawn, or glued onto the pages are all of the comments, posts, up/downvotes, etc. One of the books getting lost or damaged is when that server goes down for any of the various reasons servers go down.
And of course instead of magic, it’s the internet and programming and such.