Fatigue is a status meter that displays how well rested the player is.
Sleep Deprivation Edit
Players can rest up via all available beds, available beds can be found anywhere from inside hatches, Wastrel's or Wellie's Houses, Ruined Houses and in special areas. They only need one hour of sleep to fill the fatigue meter.
If the player were to deprive themselves of sleep in Story Mode, they will not die from it. Instead they'll have part of their stamina bar cut until they sleep again.
Sleep Deprivation in Survival or Sandbox mode however, will make the player go through the process of dying. Giving them a few minutes to regain their fatigue level before they die. They also have to sleep for more hours to fill up the fatigue meter.
In the DLC's, Fatigue is disabled, this is due to survival not being the main focus of those modes, so the playable characters never has to rest up.