The Quell system is pretty much as 9mmepiphany described it.
Your right cheek is placed on your right bicep, and you roll your head to the right until your left eye lines up with the sights. You aim with the left eye, and shoot with both eyes open.
It takes a little getting used to, but once you do get used to it, it is pretty quick and accurate to shoot with. When properly mounted, it gives basically a rifle type mount to a handgun without using a stock.
The whole point was, close range precision shooting, with the focus on one shot instant stops. The main aiming point, was the little divot on the upper lip, just below the nose in a line, straight to the rear, or along that axis, anywhere around the head. There is a nerve bundle at the base of the skull that when hit, cuts off all physical responses, including the trigger finger.
The theory was, your eyes "cross" in regards to what the brain "sees", and your left eye translates to the right side of your brain, which perceives danger differently, allowing you to be more "calm" while making the shot.
Google "Paris Theodore" and "Quell System", and you should get a bunch of leads.