Fatigue is a derived statistic that measures the condition of fatigue damage that a character can take before either experiencing unconsciousness (Fallout 3, Fallout: New Vegas) or losing Action Points (Fallout 4 in Survival mode).
In Fallout 3, Fatigue damage is only encountered as part of the "capture" sequence at the end of the quest Finding the Garden of Eden when the Lone Wanderer and their companions are incapacitated. Nonetheless, the game's engine does support Fatigue damage.
Fallout: New Vegas
In Fallout: New Vegas, the number of sources which induce Fatigue damage are limited. Only five weapons inherently cause Fatigue damage: boxing gloves, boxing tape, cattle prod, flash bangs, and Golden Gloves. All shotguns chambered for the 12 gauge shell can also cause Fatigue damage if loaded with 12 gauge bean bag ammunition.
Most sources of Fatigue damage make exceptions for robots and the Courier, as neither should ever be rendered fully unconscious. In these cases a small amount of additional standard damage is applied to the target instead. The only exceptions are flash bangs and 12 gauge bean bag rounds, which due to various bugs do not properly account for robots or the Courier.
In Fallout 4, fatigue is displayed in Survival mode. Fatigue damage occurs from lack of Sleep, Thirst, and Hunger, as well as from being Encumbered. This condition directly impacts the Sole Survivor's available Action points. The amount of Fatigue they accumulate is displayed in red on the AP bar. The more Fatigue a character has developed, the less Action Points are available. Fatigue also directly increases the risk of contracting diseases.
Fatigue is also the name of an illness (illnesses occur in Survival mode only). Having Fatigue as an illness increases the rate at which the character gets tired, resulting in a necessity for more sleep, which in turn can result in other illnesses. Like all illnesses, it can be cured with antibiotics, by paying a doctor to Cure Health, or by resting for several days.