The easiest way to explain it is to compare it to email.
You know how you might have a gmail address, your friend might have a protonmail address and your parents might still have their old aol email address? But you can all still freely talk to each other anyways?
Lemmy is like doing that, but for something like Reddit. If you notice, usernames have an @servername on the end and just like an email address that’s the server that person is connecting through. For example, I’m [email protected].
Which means I log in to lemmy.sdf.org and use their servers to read Lemmy, but I can read, post and comment on communities on any other Lemmy server that is federated with lemmy.sdf.org just like they’re on lemmy.sdf.org just like you can send an email to someone using a different email service and it makes no difference on your end.
Communities work the same way - so for example [email protected], [email protected] and [email protected] are all different communities hosted on different servers with their own separate posts, subscribers, mods etc. And users on any Lemmy server federated with the server that community is on can read, comment, post, etc (mod action notwithstanding).
This federation thing I keep mentioning is just which servers are willing to talk to which other servers - again you can compare to email. Sometimes email servers pop up to send massive amounts of spam, and when they do mail providers blacklist them and simply ignore all messages from that source. Defederating is the same idea. You use lemmy.world according to your username, so if lemmy.world defederates lemmy.ml then you will no longer be able to see any communities @lemmy.ml or read any posts or comments posted by someone @lemmy.ml - to you it will be like lemmy.ml just doesn’t exist.
If you scroll to the bottom of the page, you’ll see a link labeled “Instances”, which will give you a list of which servers lemmy.world talks to and which ones they’ve specifically blocked. Lemmy.world has a pretty long list of blocked instances.
One of the reasons I picked SDF’s lemmy instance was because they don’t block **any **instances - as far as SDF is concerned it’s up to the end user what they want to see. Also SDF is kinda a cool entity - they’re a non-profit best known for maintaining public access unix servers and a bunch of retrocomputing stuff (like dial up internet and a gopher server) that has been around since 1987 (the name is literally an old anime reference because they started out as an anime BBS).