The half pass is one of several lateral movements in dressage. While very similar to the leg yield in principle, it is considered a more advanced movement due to the direction and degree of flexion. The pony will have to flex in the direction of the lateral movement, as opposed to the slight amount of flexion in the leg yield where the pony will flex in the opposite direction of the lateral movement. During the half pass the pony will move forward and to the side in equal amounts. The pony will be travelling forward and will be flexed in the direction of pass, and in a bio-equine or four-legged pony, the pony will bend around the inner leg.
Note: In the case of a two legged pony, we usually are not able to apply leg since in many cases we are not riding the pony. I like to use the whip to mimic the actions of the leg during ponyplay. Thus, to emulate application of a rider's left leg, say, I would use the whip to lightly flick the pony's left side. Apply the whip to the side of the pony near the bottom of pony's ribcage to mimic leg action.
Now let's consider the case of a pony in a rectangular arena: while the pony will ultimately travel a diagonal path across the arena, his body will remain mostly parallel to one side of the arena as he moves forwards with a slight amount of flexion in the direction of the pass. For illustrative purposes only, think of the pony facing forward with his movement split into two separate steps: first he takes a step forward, then he takes a step sideways (either to the right or the left). You can see then how he will end up travelling diagonally even though he will always be facing forward and appearing to move parallel the side of the arena.
Above we considered the pony's movement to be split into two distinct steps: one forward and one sideways. In reality of course, the pony will achieve the diagonal movement in a single stride. So, a better way to think about this is that the pony will cross his legs as he moves (and faces) forward. Thus, if the pony is executing a half pass to the left, he will bring his right forward and cross it over his left leg such that his right leg is now both in front of and to the left of his left leg.
In most cases though the movement will not be so extreme, however the principle remains the same. Often the pony will bring his right leg forward and to the left so that it might end up directly in front of or in front a slightly to the right of his left leg.
A couple things to consider when attempting to execute a half pass:
Hopefully this explanation did not make you more confused! I will try to post a diagram here to better illustrate this movement.