Older 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.