Old article but I think it sums up the fediverse nicely for a broad audience.

But while Twitter and Facebook are controlled by one authority — a company — Mastodon is installed on thousands of computer servers, largely run by volunteer administrators who join their systems together in a federation.

People swap posts and links with others on their own server — or Mastodon “instance” — and also, almost as easily, with users on other servers across the growing network.

No single company or person, can impose their will on the whole system or shut it all down. If an extremist voice emerged with their own server, the advocates say, it would be easy enough for other servers to cut ties with it, leaving it to talk to its own shrinking band of followers and users.