A Governor is a role that can stop a lynch. This is done by PMing the mod during Twilight to stop the lynch. Many moderators will extend Twilight substantially so as to allow the Governor ample time to make a decision. If the Governor stops a lynch, the Day ends with no one getting lynched.
Because Governor can stop the Town's main weapon in the lynch, Governors are very frequently X-Shot.
Governors have been known to be able to self-target, but only if they are X-Shot.
In games where No Lynch is not allowed or whoever receives the most votes at deadline is lynched, Governor can be used to cause the person with the second-to-most votes to be lynched instead.
This role is traditionally pro-Town, but in practice can be of any alignment.
Many moderators will accept early decisions to stay or allow the lynch, so the extended Twilight is not necessarily mandatory. It may even be preferable, as Governor is one of only a few roles that require an extended Twilight.
Variations on this role change when the Governor submits their action. For instance, a Governor can submit a name at Night in order to make that player Lynchproof during the next Day. Alternatively, the Governor can submit the name of a player whose lynch they would want to halt during that Day, but cannot change their submission later that same Day.
Use and Power
Town Governors are frequently seen as Negative Utility, as stopping the lynch denies a flip to the majority of the Town. Their main use is in stopping the lynch at LyLo, hopefully catching quickhammering scum - but then, this is such a way of causing all of the living scum to out themselves that this tactic may be banned.
Mafia Governors are overpowered in normal circumstances for obvious reasons - they can delay the lynch of a scumpartner for a Day, getting the full benefits of having that partner alive for an extra Night. However, scum-side Governors only tend to appear in games where there are plenty of other ways to render someone dead aside from the lynch.