The main aim is to stop the horse from crossing it's jaw and thus evading the bit. You can have two types of grackle - the normal one or the mexican grackle. The mexican sits higher up the horse's face than the other and is fitted more tightly - thus enabling more control.
They have to be fitted properly otherwise can interfere with a horse's breathing (same for flashes).
My personal view is that they are a good noseband for a horse than does cross its jaw as they offer more control than a flash. The horses that I know who have them, have them for a reason.
I use a Mexican grakle only for hunting as my pony gets really excited and chucks her head about. She also used to get her tongue over the bit, but doesn't with this noseband.
I ride her in a loose ring snaffle, and the grakle gives me enough control to make a real difference without having to change her bit, which she gets upset about.