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 (not his hind end) leading. The horse should remain forward, balanced, and bent, moving with cadence. The inside hind leg must remain engaged throughout the half-pass, and the horse should not lose its rhythm.
The half-pass is a variation of haunches-in (travers), executed on a diagonal instead of along the wall. When the half-pass is made in a zig-zag pattern, it is called a counter-change of hand.
The Half-Pass vs. the Leg-Yield
The half-pass  requires more balance, engagement, and collection from a horse than the leg-yield . This is because the horse is bent in the direction of movement in the half-pass. In the leg-yield, the horse is fairly straight or looking slightly away from the direction of travel.
The photo is showing a Leg Yield not a Half Pass since there is no bend.
The Purpose of the Half-Pass
The half-pass is an excellent schooling movement, as the horse must engage the hindquarters and increase its impulsion. It can therefore be used as the rider is trying to increase collection or impulsion. The half-pass is also commonly seen in dressage tests, beginning at third level (USDF).
Asking for the Half-Pass
The half-pass should be performed after the haunches-in is well confirmed. It may first be introduced by riding a half-10-meter circle from the long side to the centerline, or a half-volte, and then half-passing in. The circle naturally places the horse's body in the correct bend, and helps to encourage the engagement needed for the movement.
Because the outside hind leg must step under the horse's body and push him forward and sideways, the rider should use an active outside leg slightly behind the neutral position to ask the horse to step forward and under. The outside rein maintains the correct bend and contains the energy, the inside leg keeps the horse moving forward with energy, and the inside rein guides the forehand in the direction of movement. Additionally, the rider should engage the inside seat bone, to help maintain bend.
If the horse loses quality in the movement, such as lack of correct bend (haunches leading or inside shoulder falling inward), loss of rhythm, or stiffness, the rider should straighten the horse and ride him forward.