Home is your personal feed from people you've followed (including their boosts/retweets). Local and Federated are sort of the "Explore" page (on Twitter) equiv

Home is your personal feed from people you've followed (including their boosts/retweets). Local and Federated are sort of the "Explore" page (on Twitter) equivalent, except it's chronological instead of algorithm-selected. Local is just what you said, public toots from your instance. Federated has the known public toots from other instances. These are the ones that are known to your instance because someone in your instance follows either (a) the person that posted it, or (b) a person that boosted it.