The Local Timeline
The Local Timeline only shows public posts made by users on your home instance. This can be useful if your instance has particular community norms that users on other instances may not have, such as particular topics that get put under content warnings; or particular in-jokes and shared interests.
To view the Local Timeline, click the "Local Timeline" in the Compose column or the respective button on the Getting Started panel.
The Federated Timeline
The Federated Timeline shows all public posts from all users "known" to your instance. This means the user is either on the same instance as you, or somebody on your instance follows that user. The Federated Timeline is a great way to engage in the broad chatter of the world.
Generalistic and moderated instance.