Instances are servers like lemmy.world or sh.itjust.works.
Federation is a shared language that lets the servers store content from similar servers on instances so users on instance 1 can see posts from instance 2.
A forum is a message board, they have been around since the dawn of the web. It’s like the comment section on lemmy or reddit but without threading.
Assuming you’re familiar with forums, an instance is like an individual forum (with its own topical subforums, UI, and member list), while federation is like a built-in feature to automatically cross-post threads and comments to all affiliated forums. So you can stay comfy in a chosen small forum with your favorite topics, users, and moderation culture while still being able to see and interact with content from the wider universe of all federated forums. The advantage is that the forums are independently owned and operated so no one admin can fuck it up for everybody else; if one instance gets too big for its britches and tries to pull a Reddit everyone can easily transfer to some other instance.
