Each level of Exhaustion adds 1 to your Action Load. This means that at the beginning of each of your turns, instead of resetting your Action Load to zero you would set it to your current Exhaustion Level. This logic also applies to Aspect Checks outside of combat, including Initiative.

Levels of Exhaustion can be gained in various ways such as not resting enough, because of a disease or other affliction, or by abilities where you can abuse your power.

(temporarily reduces Evasion)

(temporarily restricts movement)