This is a grappling play. That is, a play of unarmed combat, and it is done in this way. When someone flees from you and his left side is near, with the right hand you grab him by the cheekplate of the helmet, or if he is disarmed by the neck, or by the right arm behind his shoulders. In that way you will make him fall to the ground.
In this play you are moving in behind someone and pulling them backwards off their horse. They may have disengaged from a bout and you have managed to come around behind them. They may be fleeing the field and you are running them down.
The basic idea is to grab the upper right quadrant of their body and pull down to the lower left, causing them to twist away from you and fall off their horse.
There is more movement and speed here than the picture suggests. Lean forward and reach out for your opponent. Your forward motion will impel your horse to pick up speed, allowing you to catch them.
Fiore gives a number of different suggestions as to what to grab. It really comes down to anything you can get a good grip on. Bear in mind that the twist is the crux of the technique, which is why the cheek plate of the helmet is the best available option. Reaching around behind your opponent and grabbing the front of the helmet will cause them to turn their head and body fully to the right, so their back is towards you. This will disengage their hips from their horse, and start to roll their left hip up and out of the saddle. It will also cause their horse to veer off to the right.
Having taken hold of your opponent, sink your weight back into the saddle and pull your right arm back in close to your body. This will cause your own horse to slow down or possibly stop altogether. Your opponents sudden instability will cause their horse to speed up, running off at an angle. You are less pulling your opponent from their horse, as you are holding them still and directing their horse out from under them. They will roll backwards, falling onto their head or shoulders.
Throughout this whole process, use your left hand to hold firmly but gently onto your own saddles pommel. If your opponents horse kicks out, it might hit either you or your horse. As your opponent falls, your horse will either trample on or jump over them. The moment after the grab will not be the smoothest of rides, and you need to be sure you do not lose your own seat in all the excitement.