A martingale is designed to keep a pony from lifting his head up too high. This prevents a pony from throwing his head and thus may be especially useful if you have a spirited pony.
There are two main types of martingales: the standing martingale and the running martingale.
The standing martingale is usually a simple strap which connects the chin strap of the bridle (noseband of a bio-equine bridle) to the girth/waist strap of a pony's harness (also the girth for a bio-equine). Thus, the pony is head carriage is always limited to the length of the strap connecting his bridle to the waist belt of his harness. The diagram on the right illustrates a standing martingale on a bio-equine.
The running martingale also attaches to girth or waist belt of a pony's harness. However, instead of a single strap attaching directly to the chin strap of the bridle, the running martingale forms a "Y" with each arm of the "Y" terminiating in a ring. One ring encircles each side of the pony's reins. Thus, the tension and position of the reins dictate how much the pony can lift his head. The diagram below illustrates a running martingale on a bio-equine.
Martingales are great tools to keep a pony from tossing his head, but keep in mind that in some cases you will your pony to keep his head up high, and in those cases, a martingale will be do more harm than good. It all depends on the flavor of ponyplay you want.