You can compare the home timeline to the normal timeline on Twitter of the people you follow across all instances. The local timeline, as the word suggests, shows you all posts from people that are on the server on which you are registered. You can compare this to the Twitter firehose of all tweets from everyone on your local server. And finally, the Federated timeline shows you all public posts from people on yours and all the other servers of the decentralized network that are connected to your server.