quickness of mind; mental agility; wit
Refers to how quickly and sharply one thinks, processes information, or comes up with ideas. Often used in phrases like 頭の回転が速い (quick-witted) or 頭の回転が鈍い (slow-witted).
He's quick-witted, so he can answer any question right away.
Lack of sleep dulls your thinking.
Compound of 頭 (head, mind) + の (possessive particle) + 回転 (rotation, revolution). Literally 'rotation of the head', metaphorically referring to the speed at which one's mind works.