Best analogy I’ve heard is to think about email. I’m using gmail, maybe someone else uses yahoo, and maybe a third person has their own mail server set up at home. We can all send each other emails, and the content of the emails will largely look the same, despite that none of us are accessing it through the same site.
Another example; since you’re over on kbin; I’m on Lemmy.world right now. I can still see your posts and comments and you can still see mine as though we’re both browsing the same website.
Why is that important? Basically it keeps any one person like Spez from having complete and total control over the entire “site”. Since the “website” is actually a lot of websites made to act like one big one; each individual site has its own server, admins, etc. and if one goes down, or has admins that go on a power trip; it won’t totally ruin the experience for everyone on the fediverse; just that one server.