I’m a software dev and don’t think I fully have a handle on it. Basically the Fediverse proper is all of the servers networked to each other via the ActivePub protocol, which is to say that they have agreed to share activities (or rather posts with each other) on a peer-to-peer basis. Where it gets a bit more complicated is that there are applications like Mastodon and Lemmy that use activitypub in a particular way to create a specific flavour of social network, so most Fediverse instances are one of these - same executable, many machines - and these only connect with other nodes that are either the same, or compatible with the activities they share.

In principle this means that power over the network is not concentrated in the hands of a few, as instance owners who cause trouble, or fail to moderate their hosted users, can simply be blocked and routed around. An instance can be public and host to anyone who wants to sign up, invitation only, a self-hosted individual, or any kind of organisation (this is where the email metaphor is strongest).