The best analogy I’ve seen is that each instance is like an email server. You can open your email with Google, Yahoo or wherever you want, you can still communicate with other people in other servers without any issues. If Yahoo goes down, Gmail will still work, if Gmail decides to ban nsfw attachments, yahoo can still decide their own rules. That’s what being federated means roughly.
The best analogy I’ve seen is that each instance is like an email server. You can open your email with Google, Yahoo or wherever you want, you can still communicate with other people in other servers without any issues. If Yahoo goes down, Gmail will still work, if Gmail decides to ban nsfw attachments, yahoo can still decide their own rules. That’s what being federated means roughly.