Barn shorthand for a horse's ability to anticipate a cow's next move: it reads ears, head carriage and weight shifts, and reacts before you do.
In cutting you separate a single cow from the herd and keep it from getting back — a run lasts two and a half minutes. The remarkable part: during those minutes the horse does the work. Cow sense is the ability to read the cow's body language — ear position, head carriage, weight shifts — and react before it moves. It's partly innate, partly trained on real cattle; a sales ad claiming it means nothing until you've seen it on a herd. For you in the saddle it mostly means: don't interfere. And on the safety side, this is exactly where riders come off — the turns are abrupt and unplanned. Sit deep, don't hold on by the rein, and learn it on settled cattle rather than fresh ones.