If you run a Mastodon server, you can optionally show visitors who aren't logged in your server's Local timeline or Federated timeline through the "See what's happening" link on the front page of your server's website.
To switch on your server's "See what's happening" link, log in through your server's website and go to Preferences > Administration > Site Settings > Allow Unauthenticated Access To Public Timeline, then tick the box and click Save Changes.
To choose between showing your site's Local or Federated timeline, go to Preferences > Administration > Site Settings > Include Federated Content On Unauthenticated Public Timeline Page, and then make the following choice: to show your Local timeline to the public UNTICK this box, to show your Federated timeline to the public TICK this box. After making your choice, click Save Changes.