I dont know how tech saavy you are so apologies if this is an oversimplification but:

Matrix is a protocol. Think of it like a language. There are different matrix backends (synapse, continuwuity, etc) that run the server, which speaks the matrix protocol. Anyone can make a server and host it. They can open it up to federate, which lets other matrix servers talk to that server.

To join matrix you pick a server (matrix.org has one but there are many more. Some fediverse servers like bark.lgbt and blajah.zone have their own matrix servers under the same name). You sign up for that server same way you did for lemmy.

Then you pick a client. Element, cinny, sable, fluffychat are a few. These all “speak” the matrix protocol, the way something like the voyager app speaks activitypub, the protocol for lemmy. They all have slightly different features so use the one that has the features you like.

I love matrix. I self host my own but started on matrix.org. ive migrated my D&D group and friend group from discord to matrix.

if the server you join supports it, you can also bridge discord, telegram, and other chats to matrix. I still talk to some people on fisvord through a bridge.