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
Following users on remote instances who you meet on the Federated Timeline can lead to meeting more users on more instances and further connecting your instance to more and more of the entire Mastodon and OStatus network.