What is the Fediverse?
The Fediverse is a network of connected websites that, together, make a full social network. Individually, each website may service as few as one user, or as many as one million users. When these websites are connected to each other, it enables interaction online without a single point of failure, and without a single set of admins or moderators.
Each website in the fediverse, called an "instance," is moderated by the people who maintain the website. This allows for different kinds of communities to be cultivated. For example, the instance asonix.dog is run by @asonix, who is the moderator of the users on that website. @asonix sets the rules for participation on that instance, and people are welcome to sign up there if they agree to follow those rules. If those rules are not amenable, users are free to sign up on other instances with different rules. Since these instances are connected, certain moderators may choose to mute certain other instances or certain users on certain instances, to make sure the content on the instance they run meets the standards set in their rules.