A federated system consists of multiple instances (ie: lemmy.ml, lemmy.world, feddit.de, etc) that are able to communicate between eachothers using a standard communication protocol (in this case ActivityPub). This mean that each users in all of those federated instances are able to see and interact with eachothers by posting, commenting, and subscribing to local and remote communities.
Think of it like the email system. You’re able to get an email account with Gmail, but that doesn’t limit you from sending emails to users at Hotmail, Yahoo, etc.
Let’s say you’re on Lemmy.ml (which is an instance) and there’s another instance (example.com) with users that are consistently disrupting the communities in your local instance. The instance admin reach out to the other instance admins, asking them to get their users to follow the rules of the local communities and the instance, but despite banning these users and removing posts and comments, the situation persists. The instance admin may decide to push the nuclear button, and deny the unruly instance from being able to communicate with it. This makes all communications between these two instances impossible, and all posts, comments and user content that was synced will remain visible (unless the instance admin does a cleanup), but all new content from that instance will basically never show up.