To balance and steady the rhythmic motion.
I don't use it for complete collection though. My guy is trained to collect, by a light pressure with the calf and being driven by my seat, to gather up the hind end, and a slight raised position of my hands, and he steadies and drops his head. (Mind, he's also trained in Western Pleasure. Different worlds, and different headsets. Yet, he distinguishes to two, but is still balanced through both positions).
Half halts, I use to engage, and bump them off their forehand. Also good for speedy horses. When they get speedy, they get flat. A half halt brings them back down, to a balanced pace and position.
Atleast, that's what I've always interpretted it doing.
"You're just as sane as I am."~Luna Lovegood.