The half-pass is a lateral movement seen in dressage, in which the horse moves forward and sideways at the same time.
Unlike the easier leg-yield, the horse is bent in the direction of travel, slightly around the rider's inside leg.
The outside hind and forelegs should cross over the inside legs, with the horse's body parallel to the arena wall and his forehand leading.
At higher levels it is used to perform a counter-change of hand, combining more than two half-passes with changes of direction in a zig-zag pattern.
The circle naturally places the horse's body in the correct bend, and helps to encourage the engagement needed for the movement.