If you're fatigued, you're exhausted. You're bound to be fatigued after climbing a mountain — or babysitting for five year-old triplets.
When you're so wiped out and tired that you can barely brush your teeth and fall into bed at night, you're truly fatigued. It's another way to say "tired," "exhausted," "beat," or "tuckered out." The adjective fatigued comes from fatigue, originally a French word meaning "weariness," from the verb fatiguer, "to tire," which has a Latin root, fatigare, "to make weary."