Silence is one of the states that an account can be set to.
When your account is silenced, you cannot set the visibility of your notes to Public. Home, Followers, and Direct are still selectable, so even if your account is silenced, followers and direct visitors to your page will still be able to view your posts. They will just not be able to view them in the GTL (Global Timeline) or LTL (Local Timeline).
The silence status of an account is set by the instance moderators.