The recurve design is credited to the Mongolians, who used the bow on horseback. The bow’s design has two distinct advantages. One, it’s short stature allows one to easily pass the bow from one side of the horse to the other, thus allowing the archer to shoot on the horse’s left or right. Most other bows are too long for this, limiting the archer to shooting from the horse’s left (if the archer is right handed). Secondly, the curve of the bow’s limbs form pads that stop the string in a more sudden fashion. Thus, the impulse delivered to the arrow is higher, giving the arrow a high initial velocity.
http://mongolian-bow.com/history-of-the-recurve-bow