It’s really a lot like email, only the messages are (mostly) public instead of private.

If you have an account at gmail.com you can send and receive emails with someone at another site like mit.edu, because your mail server and their mail server know how to talk to each other (that’s “federation”).

But you don’t have to personally log into their mail server to do that. You just use your account on your server, and the servers take care of getting messages to the right server for the recipient.

Similarly, here, you can subscribe to and comment on forums (“communities”) originating on other instances. You don’t have to personally log into the other instance to do that; the servers take care of that part.

You can use your account to comment and post on communities on other instances. This does NOT mean your login will work on their site.

If you go to https://Lemmy.ml/C/mildlyinfuriating@lemmy.world you are now interacting with a community on that instance. The posts, comments and votes are synchronized across at a server-to-server level and cached in Lemmy.ml

I would get an account on a different instance anyway though, lemmy.ml is overloaded and needs people to spread out to different servers

You only need one account and that will allow you to post and comment on other instances.

That’s not how it works :) Your lemmy.ml account is tied you this specific instance.

IIRC they are looking into an option to transfer your account between instances but I might be wrong.

No, each instance has its own database of users so you’ll need a separate user for each instance. However, as you pointed out, you can subscribe to communities, comment on posts, and upvote/downvote posts on an instance with an account from any other instance that federates with it.