The fediverse is a loose cooperative (or federation) of independent servers which can choose to communicate with each other (or not — in the case of bad actors or chronically under-moderated instances). These servers do not operating a single type/brand of software, but rather run many different services that all share information via the "ActivityPub" standard. There are federated equivalents for "X" (Mastodon), Facebook (Friendica), Instagram (Pixelfed), YouTube (PeerTube), and others, an...
