An instance is a server that provides both a place to login and communities to browse.
You can have a account on Lemmy.World, but browse and comment on communities on servers such as lemm.ee. Likewise folks that have accounts registered on lemm.ee can post on communities on lemmy.world.
The servers talk to each other via the ActivityPub protocol. I've seen folks use the email analogy, but I think it confuses more folks referring to it like that.