The fediverse is a decentralized social network comprised of independent servers (called instances) that can talk to each other. When you’re registered on one fediverse site, you can see and interact with users and content on many other fediverse sites, depending who your instance connects to and who is blocked, also what other platforms the service you’re using is intercompatible with (think the differences between Twitter, Instagram and YouTube, all of which have “clone” platforms on the fediverse that you can just download the source code for and host on your own server). Each instance can focus on a specific niche or topic, or they can be general purpose, and all of them can make their own rules (though the toxic or offensive ones tend to be blocked by many or maybe even most other nodes in the network). The main problem the fediverse tries to solve is problem of a single point of control. For example, Reddit’s administrators have absolute control over the site, which means they can do anything they want on it, often with the main intent being profit. The Fediverse aims to spread that control over many people by allowing independently controlled servers to communicate with each other, so if instance’s administrators does something atrocious, people can simply move away from that instance and even block it from communicating with their own instances. Is it perfect? No. Does it still have a lot of problems? Yes. But in my opinion, it’s better than traditional social media platforms where a single for-profit company controls everything.

Lemmy isn’t a fediverse platform yet, but federation is being actively developed. It’s designed to be a Reddit-style forum with nested comments and independent communities. You can basically think of it as a Reddit clone that plans on becoming decentralized. Such a platform is currently missing from the fediverse, which is why Lemmy exists.