In use, mastodon feels more or less like twitter. There are some differences - no “quote” tweets unless your client offers that, if you mention someone with @ in a DM, then they get dragged into the DM ( causing awkward situations for those who don’t realize it), and timelines is always chronological. The “federation” thing just means that anybody can set up a server (just like an email server), and as long as the servers are willing to talk to each other it makes no difference to the users. You can see toots from other servers, etc. You can also move your account from server to server as you wish.
Mostly it feels just like twitter to users, except a little jankier (servers are struggling under the influx of new users, and having to figure out what server to sign up for can cause confusion to new users).