This is the simplest and, in my opinion, the best move in equestrian. I have found it to cover almost every situation in almost every discipline.

If the horse is lively, not listening, dull, scared, fresh, boisterous, feeling his oats, or not concentrating the half-halt can be used. If you are attempting to piaffe, passage, execute a flying change, shoulder-in, half-pass, or leg yield, if you are exercising your horse across a wide, green paddock, or creating a perfect circle in an arena, or approaching an oxer, a cross, a vertical, a corner fence, a brush, a water, even trot and canter poles, the half-halt can be used.

It is designed to balance, re-engage and to create lightness throughout the horse's body. It is a pause, a comma, a break, a "re-listening" in the horse's pace, a signal that something is about to be carried out.

My instructor used to say to me that if, at anytime, I felt that the horse was not on a straight line, or straight on a curved line, if he was going too fast, was not balanced, too hurried, if I was losing contact, if his head was too low, too high, if I wanted more impulsion, rhythm, tempo, bend or flexion I should half-halt. Sometimes she would tell me to half-halt every stride until the horse was `right'.

Basically, there is a golden rule: If in doubt, half-halt.

The execution of a half-halt is both simple but difficult. The steps are simple, but they can neither be carried out at the exact same time or more then a second apart.

First step:

You give with the inside rein (the right rein when travelling clockwise) while tugging gently at the outside rein. The inside rein must be relaxed to allow this to work, but the tug on the outside rein is the basis of everything else. This should straighten the horse and bring his attention back to you. It should also turn the horse head slightly to the outside.

Second step:

It must be executed right after the first. With the inside leg, push the horse forward. If you are wearing spurs, do not use the spur. The horse should immediately steps up into the bridle at the desired pace, with his hind legs coming up underneath the saddle. If this does not happen then push harder with the inside leg, or, to get the hind legs underneath the horse, put your inside leg further back so that it feels, to you, that your leg is on the flank, or use a dressage whip to tap him on his hindquarters. If this does not work, your horse is lazy or you have not worked him into the right pace,so you'll have to go back to the good old warm-up routine of kick, whip, kick, whip, until the horse goes.

Of course, the half halt should be learnt with a professional and not from a node. And if these steps don't work, there is the chance that you horse is not trained to half halt. So, again, consult a professional.

If there's anything I have missed, or you think that I have it completely wrong and I am sure I have, please add it, or message me. I would hate for a horse or rider out there to be confused due to a poor writeup.
Oh, and if you don't understand any of this, it's probably because you don't ride horses.