It consists of a strap around the horse's neck, from which one strap runs to the noseband of the bridle and the other between the front legs to the girth.
Fitted too tightly, a tie-down can restrict a horse's movement - it should be fitted to only come into play if a horse raises his or her head too high. And although a lot of people do it, traditional wisdom says it should never be used when jumping. (You see them a lot in hunter classes in America, but real hunt people use a running martingale, which I'll talk about on Monday).
Barrel racers use tie downs because they feel they help the horse brace better during extreme turns. (Some barrel racers, however, believe in not using them because they think the horse becomes dependent on them). In this case, the tie down strap is connected to the breastplate. (Using a tie down without the neck strap is incorrect and potentially dangerous).
Another use of a tie down is as a temporary training aid if you have a horse that is throwing his head all the way up - for the rider's safety (I knew somebody who got her nose broken that way). Unfortunately, some people use them as a substitute for teaching the horse not to do that...which as its often caused by over bitting, anxiety or lack of fitness, is not a good idea.
A show hunter wearing a standing martingale. Source Paul Keleher via Wikimedia Commons.