Bay is one of the three base colors of a horse. These horses have a red coat with black points, including the ears, legs, mane and tail.
A bay horse has at least one copy of the dominant extension gene (Ee or EE) which makes the coat black and the dominant agouti (Aa or AA) which makes the black stick to the points.
This isn't the only way the bay coat is expressed however. Wild bays' black legs don't go all the way up, and seal bays, like the one pictured below, look almost black with some brown in spots like the muzzle.