An instance is basically a Lemmy “app”. These “apps” or instances of Lemmy are being run on some server somewhere. Could be your own server you set up or a pre-existing one like lemmy.world setup by someone else. Each instance or “app” is also connected to every other Lemmy instance unless explicitly blacklisted. This why you sometimes see urls in peoples user names and communities. They’re posting from someone else’s Lemmy server (not the one you’re logged in to).

The idea is if one instance goes down, Lemmy as a whole will continue to run so long as one is still running. It also allows people who to host their own for whatever reason they may have, whether that be differences of opinion with existing instances or simply because they want their own set of communities.