The quarters of a horse are the hindquarter region: the hips, croup, and upper portions of the hind limbs that generate the primary propulsive force in locomotion. When evaluators describe a horse as having “good quarters,” they mean the hindquarters are well-muscled, broad, and angulated to produce powerful engagement. The croup — the topline from the hip joints to the root of the tail — is the roof of the quarters; its angle and muscling affect how efficiently the hind legs reach under the body.
The quarters work in conjunction with the hock and stifle joints to drive movement and support collection. In disciplines requiring impulsion — reining, dressage, jumping — the depth and muscling of the hindquarters are evaluated alongside the angle of the pastern and the structure of the hoof as part of a complete conformation assessment. Weakness or lack of muscling in the quarters (often called “goose-rumped” when the croup slopes too steeply) can limit a horse’s capacity for collection and power.
In the broader anatomical map of the horse, the quarters are one of the key evaluation regions alongside the withers, back, and chest. The term can also appear in the phrase “quarter crack” — a vertical crack in the hoof wall at the quarter, which is the side of the hoof between the toe and the heel.
Further Reading: Wikipedia’s article on horse conformation covers how the hindquarters are evaluated alongside other structural regions in a full conformation assessment.