Wikipedia
Haunches-in, also called travers or tête au mur ("head to the wall" in French), is a lateral movement used in the dressage discipline of horse training. It has a close cousin, haunches-out, renvers, or croupe au mur ("rump to the wall"), that is slightly more difficult. Both movements are four-track, meaning they produce four lines of hoof prints in the sand, as opposed to the usual two seen if the horse is straight and to the three-track shoulder-in.
In haunches-in, the horse bends its hindquarters slightly to the inside of the arena, away from the arena wall, so that the horse is bent in the direction of movement. The front legs and shoulders should not move from the original track. This produces the four tracks, with the outer track made by the outside foreleg, the second track by the inside foreleg, the third track by the outside hind leg, and the inside track made by the inside hind leg.
In haunches-out (renvers), the horse is similarly bent in the direction of movement, but the hindquarters are bent toward the arena wall instead of away from it. This produces a four-track movement consisting of the outside track made by the outside hind leg, the second track by the inside hind leg, the third track by the outside foreleg and the inside track by the inside foreleg. This movement is considered to be more difficult than travers.
A horse that naturally moves with its haunches slightly to the inside is simply travelling crooked, and is not performing haunches-in. These horses usually lack correct bend through the whole body, do not work properly into their outside aids, and do not show the same engagement or balance seen in horses ridden in a true haunches-in.