Federated Universe, or open social web as some have come to call it. It refers to many services that use the same protocol ActivityPub for their backend. Different software uses it a little differently but a shared backend is how for example you can get people commenting here from their Mastadon or Mbin account.

It can be tough to describe without getting too much into unnecessary details. Other big things is instances. Basically anyone can download the hosting software for one of these sevices such as Lemmy. Once it's run it becomes and instance of the Lemmy software and then connects to the broader network of Lemmy servers.

Hope that didn't make things more confusing. The main benefit for you is if you find you disagree with the admins where you signed up you don't need to abandon the platform as whole, you can just look around for an instance that's run in a way that more aligns with your views.

My instance, while one of the biggest, is small enough that I can directly chat with the the handful of admins if I have any concerns or questions. This works for me. Plus it being hosted close to me is good for latency.

Edir: and happy new year to you too! Hope you enjoy the time you spend it here.