Two-point position is a phrase used to describe the position that a rider takes as they are approaching a horse jump As a rider is preparing to go over a jump with their horse, the rider will move forward and into two point position- they will be riding with two points in connection with a horse. The two points are referring to the contact on each leg on each side of the saddle. This photograph shows a rider riding in two-point as she approaches a horse jump.
Before learning to jump, your instructor will teach you to maintain two-point when not jumping. Two-point takes considerable balance and muscle strength, and should be practiced before a rider learns to jump. In two-point the rider doesn't just lean forward over the horse's neck, but balances their weight farther back over the seat of the saddle. In this way the rider isn't off balancing the horse, but is centered over the horses body in a slightly crouched position.
This photo shows a horse rider in two-point position