Answer: there are probably better people to explain Lemmy specifically than me, but I went down the Fediverse rabbit trail when Mastodon was being talked about as a Twitter alternative so I think I can get the basics down.

Fediverse is a collection of servers which all agree to use the same communication protocols. This allows them to communicate with each other even when they aren’t run by the same company/organization. You can’t see someone’s Facebook post on Reddit or vice versa (screenshot apocalypse notwithstanding) because Facebook and Reddit haven’t agreed for their sites to be able to communicate with each other. The Fediverse is designed to allow different people hosting their own Fediverse servers to be able to interact with each other.

Lemmy is (to the best of my knowledge) a specific subset of the Fediverse designed to replicate the same kind of interactions seen on Reddit (communities => subreddits, post/comments, upvotes/downvotes, etc). So anybody can create their own Lemmy instance, and interact freely with all of the other Lemmy instances.

TECHNICALLY a Lemmy instance can even interact with other Fediverse instances not using Lemmy (Mastodon for example). But I’m not quite sure how that works given that a Mastodon toot doesn’t have the same structure as a Lemmy post