There are several reasons for using a noseband on a horse. It helps keep the mouth quiet, enhancing communication; it discourages evasion of the bit; it provides an anchor for a standing martingale; helps hold the bridle in place; and balances the look of the horse's head.
There are different types of nosebands, but the basic one is known as a cavesson, designed to encircle the horse's nose just below the cheekbone. A well-trained horse that accepts the bit easily will perform well with a simple cavesson.
A crank or cinch noseband is the same as a cavesson with the addition of a lever mechanism under the chin, allowing for a tighter fit , which improves performance especially in top level dressage.
Flash nosebands have a thin strap dropping down below the bit, secured under the chin groove, which effectively keeps the horse's mouth closed, better engaging with the bit. The flash is the norm for show jumping and schooling.
Drop nosebands encircle the nose at a lower point than a cavesson and are useful for young horses still in training.
The grackle or figure-eight noseband fastens behind the upper jaw above the cheekbone, crosses the nose diagonally and fastens again under the chin groove. The high position allows the horse maximum air intake and is probably more comfortable for the horse.