According to Wikipedia, Dressage is a competitive equestrian sport, defined by the International Equestrian Federation as "the highest expression of horse training", where "horse and rider are expected to perform from memory a series of predetermined movements."
The word 'dressage', is French and loosely translates to 'training'. A young horse, trained in 'dressage' learns to carry a rider, carrying his own weight when doing so. As his training progresses and his body builds in strength, the exercises become more complex, incorporating movements that once allowed a rider to attack the enemy and escape if required. Dressage has become a specialised discipline in it's higher form but the basic exercises suit every discipline a horse may be used for.
Below is a video of the current World Champion Freestyle partnership of UK rider Charlotte Dujardin and the Warmblood gelding Valegro.
The image above is based on an image of a Thoroughbred mare competing at a show. Thoroughbred's were once the kings of the Dressage ring but horses of Warmblood breeding, such as Valegro, now dominate the international competition rings.