Compare: a horse acting silly at a show, can't stand still. The normal tendency is to scold him, like "Stop that! You know better! What's the matter with you?"
The NH way is to try to see it from the horse's point of view: he doesn't "know" anything, he's just responding to everything. You move on to trying to get his attention, and/or simply moving his feet in a safe direction (usually a circle) until he can get himself together again. Or some other way, but the point is, you trying to see it from the horses' point of view.
I'd say every good horse-handling these days is NH--- but that's not so. Most everyone I see at shows STILL act as though their horses "know" what they're "supposed to do." Not that these people can't handle their horses, they do, usually with physical restraints. And a lot of them still believe that horses will NOT do something to AVOID being hit.
In NH hitting/not hitting; rewards; release, etc. is really not like human-concept punishment/reward. It has to do with logic, horse-logic.
Parelli and others have "games" and whatnot, mostly as exercises to teach humans this logic, though lots of it can be useful too.
Okay, that's my opinion!