On this page you see examples of websites you can host yourself. I'll use Mastodon as an example since I've used it. I know about hubzilla slightly but have not used it.
Mastodon is a platform you can run on your own server. That server you're running is called an instance. You can also register on an instance someone else is running.
Think of a single Mastodon instance as a clone of Twitter. One nice thing is: Your server, your rules.
Then, you can also allow your Mastodon instance and its users and their posts to be discoverable by other instances.
I think it's said to be federated because no one entity controls the content that is being shared. the information is passed around from instance to instance by rules that are defined on a per-instance basis.