File:Mastodon timelines.png

English: Mastodon is an open-source alternative to Twitter, where anyone can start and run an "instance" of many individual members on their own server. Posts are not automatically pushed to all other instances in existence, and instead propagate to only the instances of people who follow them. Those posts are visible only in particular locations to particular people in particular circumstances. It is difficult to describe, and much easier to express and learn about with a diagram. This is that diagram. It doesn't contain every circumstance in which a post is propagated and visible, but it contains most of them.

Image description:
Title: What makes up each timeline?
Text: This flow chart might help explain.
To look at it from the other direction: Your public toots will always be in your instance's local timeline. If even one person from example.instance follows you, your public toots will be visible in the federated timeline for everyone on example.instance.
(Replies don't make it into the public or federated timelines.)

Flow chart:
Start: Public toot by @Foo.
Am I following @Foo?
Yes: Toot shows in Home timeline.
No:
Is @Foo on my instance?
Yes: Toot shows in Local timeline.
No:
Does someone on my instance follow @Foo?
Yes: Toot shows in Federated timeline.
No:
Did someone on my instance boost @Foo's toot or search for it with its URL?
Yes: Toot shows in Federated timeline.
No: @Foo's toot never reaches my instance.

If you choose "unlisted" instead of "public", your toots will be seen by followers and be visible on your profile but they won't appear in the timelines.