The half halt is re-balancing. In its elementary form, it connects the horse - hind legs stepping under, back engaging up, neck stretching up and out into the receiving hand. As training advances, the half halt collects the horse, shifting the horse’s center of gravity toward the haunches.
On the part of the rider, the half halt is a combination of seat, leg, and hand asking for this effort from the horse. The seat lifts the horse’s back and sets the rhythm. The leg keeps the horse’s hind leg active and stepping towards the hand. The hand, supported by stable and supple torso and arms, says “stay here.” Not backwards, “here,” in order to catch the energy generated by the efforts of the haunches and channel it into a more connected/collected balance.