@Blueteach Imagine if there were 100 different Twitters. Each of those is an instance. Local timeline is the one you signed up on, but you can choose to read the federated timeline, I.e. combination of all instances.
@Borogove not a full union though -- federated timeline is all messages from people you follow, on any instance, any reply to those messages, and any message the mentions you, sent from any instance.