So I've found that it's helpful to think of federation similar to email. Email is a protocol standard that anyone can implement. I have a gmail account and I can send and receive email to anyone with an email account, even if they don't use Gmail.

I think of it as website forums that connect together, every site and member can block/allow whatever they want.

Like others have said, Lemmy runs off of ActivityPub, an open-source protocol similar to Email. Some other applications, such as Mastodon, Kbin, and PixelFed, also use ActivityPub, which is why you can occasionally see posts from those apps if a Lemmy-user shares them.

"Easier Moderation" and "Protecting data" are good, sure, but the main benefit of Open-Source, Federated Social Media is the decentralization and taking power over media away from corporations.

Imagine if Email was closed-source, like Reddit. In order to send or receive email you had to make an account on "Email.com", the email corporation could read your private messages to "moderate", they could ban your account if you send emails they disagree with.

And you might say, "But I use Gmail, and Google can do all those things!", and that's true! And the same is true for Lemmy.world or, yes, even Hexbear.net. What makes Email (and ActivityPub, which Lemmy uses) different is that you can rent a domain name from Mali, set up a computer in your basement, and host your own server. And you can send emails from "ComradeDrew@ComradeDrew.ml" just as easily as you can ComradeDrew@gmail.com.

And just like I can send an email from my own private email server to someone with a Gmail account, you can send a private message with a Hexbear account to Lemmy.world (or, even, Mastodon social or Threads.net, assuming neither party explicitly blocks traffic).