A martingale is generally used to control the movement of a horse's head while riding, particularly while schooling or training a horse.
There are different types of martingales for different purposes.
The most simple is the standing martingale, which exerts pressure on the nose if the horse tries to raise its head too high, helping the rider maintain balance.
A running martingale is connected to the reins, works in conjunction with the bit, and is less restrictive than a standing martingale.
A similar device to the running martingale is known as the Market Harborough, which provides good control by applying pressure to the horse's mouth through the bit. This is used mainly as a training aid.
Another type is the Irish Martingale, which offers no enhanced horse control or restriction of head movement, but is purely a safety aid, designed to prevent the reins from sliding over the horse's head if the rider has a fall.