A very brief, very simple overview of Mastodon (As I understand it)
It is open source software so anybody with their own web server can set up an instance - there is no one Mastodon site, there are many.
Each of these instances can connect to other instances, so if you sign up on one instance, and that instance is connected to several other instances, then you can follow and post to other people on those other instances. This is where the federated concept come in.
The fact that there are multiple instance is one of its strengths. No one company has access to all your data.
Also if one goes down, then you can sign up on another instance, although I think you'll lose your messages (I'll have to check). But this is also one of its weaknesses.
You can choose which instance to sign up to, but again the potential problem is if the owner of the instance can no longer run it for whatever reason, the instance will disappear.
This explains it a lot better
A thorough introduction to Mastodon
mastodon.help
One more thing. One reason why Mastodon is 'slow' is because of the exodus from Twitter and the majority are signing up on the most popular instance - mastodon.social - so that site is getting a lot of traffic
If you want to try it out, I suggest one of the small to medium instances. but choosing which one