I hadn't really thought about it, but Spyder's right - most folks have some idea about the cues but aren't really clear on what the biomechanical result should be.
I was very lucky to attend a wonderful clinic by Elizabeth Lewis early in my dressage education where she did a demo on the half halt.
Elizabeth usually began and ended her clinics with a mounted demonstration, which she would narrate/comment on from a lapel microphone.
I can't tell you enough what a wonderful teaching technique this is - to be able to see a horse and rider at that level, and have the rider explain what she's doing while she's doing it - it's incredible.
This time she was on her current Grand Prix horse, Dream Dancer. She demonstrated half halts on Danny, ranked them in intensity from 1 to 10. A "1" or whisper half halt was barely perceptible to us on the ground, other than Danny appeared a little lighter. A "10" half halt actually produced a pause in the rhythm of his trot and he visibly sat down more on his inside hind - it was somewhat comicial to watch. I had a little momemt of clarity when I saw that and suddenly understand how a half halt prepared a horse for pirouettes and helped produce passage. It was also when I finally understood what "through" meant - on a horse that's not through, the half halt only affects the front end. "Through" means the effect of your aids goes all the way through the horse's body, hence the extra "sit" behind. Also, once I had seen the "10" half halt and it's effect, it was much easier to see the lower intensity ones and their effects.
So to anyone who's struggling with this concept and has access to a coach who's riding or competing at a higher level, ask them to do a similiar demonstration for you.