So, your full username includes the server (also called an instance), in your case it’s Eisenworth@lemmy.world which means lemmy.world is where you’ve created an account. You can freely make accounts at other instances if you like also.
You might notice that it looks like an email address, that’s on purpose - email is the usual example of a federated service that people are familiar with: if you have a Gmail account you can still send and receive messages from people with a Yahoo account, or protonmail, or AOL, or whatever. In fact it’s possible to run an email server yourself, and that can also be done with software like lemmy also. Lemmy is one particular piece of software a server can be running that can connect to this network, there’s a few others like Piefed and Mbin that all work together, but whichever one a server runs, the users can see the same communities and posts and comments. (Exceptions exist when server admins block certain things for various reasons)
Which instance to choose mostly doesn’t make much difference, but there are some that host communities for specific countries or languages, some that are politically extreme far right or extreme far left (to the point of being authoritarian communists - notably the developers of the Lemmy software run such an instance, lemmy.ml), but any instance’s politics only go as far as communities hosted there and users from there. I feel this one (.world) is a decent balance. Note that you can still see communities and users from other instances, except as noted below.
Another consideration when choosing an instance are which other instances it blocks (“defederates”). For example there’s one called Beehaw which is probably a nice little community, but they have cut themselves off from most of the big instances, so if you log in there you won’t see posts from here.
FuglyDuck@lemmy.world 3 hours ago
In brief… your username is listed as Jack @ lemmy.world
everything after the @ is the server they’re on. If you don’t see that, they’re also on the same server as you (so my name shouldn’t also include @lemmy.world the way Funkycarrot’s includes @discuss.tchncs.de