To elaborate further from the other comment, it's a person running a copy of the Lemmy software on their server. I for example am running mine (and seeing this thread) from https://zemmy.cc. Thanks to Federation all of our different servers are able to talk to each other so we can have a shared experience rather than everyone being on one centralized instance managed by one set of administrators (like reddit is).

This provides resilience to the network. If reddit goes down, reddit is down. If lemmy.world goes down, you can still access the content of every community that isn't on lemmy.world, and if other servers were subscribed to the content on a community from lemmy.world you could still see the content from before the server went offline (and it will resync once it's back up).

If we put all of our eggs into a single basket, we have a single point of failure. If all of the major communities go to lemmy.world then lemmy.world is that single point of failure. Doing that is effectively just recreating the same issues we had with reddit but with extra steps. By spreading larger communities across servers we ensure that the outage (or permanent closure) of a single instance doesn't take down half the active communities with it.