I have no idea where it originated but when you want a horse to stop we’ve all learned to say “whoa”. Except in dressage where no verbal commands are allowed. Unfortunately horses don’t grow up naturally knowing what whoa means.
Beginners typically try to pull back hard on the reins and yell at the top of their lungs. As you might imagine the horse interprets this as “DANGER my rider is scared” and starts moving forward much faster.
Good cowboys only need to shift their weight backwards by slumping a little bit and planting their rear end into the saddle. Sometimes people say “sit on your W” and by that they mean sitting on the rear pockets of your jeans (wrangler jeans have w shaped stitching on the pockets). I think of it as just heavily planting my rear end through the saddle into the ground. I don’t tighten my reins at all.
Although horses already know how to stop without our help the skill is in teaching them to stop on cue. And sitting “down” is the most accepted way to do that. So in the beginning you teach it at a walk and with gentle but firm use of the reins and bending. Just before it starts to stop sit down and then really reward the horse when it does it right. Many many repetitions later and after practicing at increased speeds the horse will eventually learn what you want.
What you want is for the horse to come to a complete stop within 1-2 strides. The horse should stay calm and lower it’s rear end, put both rear feet forward and try to plant those rear feet into the ground sort of skidding until a complete stop is achieved, then rise back to a normal position. It’s beautiful when done correctly.
And in case you haven’t figured it out already, stopping is one of the first things you want to teach your horse!