The concept works like this. You keep both eyes open as you scan for targets. The eye looking through the scope will see a more blurred image than the eye that is not looking through the scope while the scope is in motion. This is due to the magnfication. In this situation, the brain selects the image from the eye that appears to be less blurry. But, the reticle in the ACOG is illuminated, so the brain superimposes this reticle on the vision signal from the eye not looking through the scope. This allows you to very quickly acquire the target, effectively making the 4x scope act like an unmagnified Aimpoint.
Now this is where the really cool part comes in. As you acquire the target, the motion of the scope slows down to a point of almost being steady. When that happens, the image from the eye looking through the scope becomes very clear, and your brain switches to this vision signal instead of the unmagnified eye image. Now your target is magnified at 4x, and you can do small aiming corrections for the perfect shot. You still keep both eyes open, even in this phase of aiming.
Basically, the ACOG's with BAC are the best of both worlds in my opinion. With training, they are just as fast as Aimpoints, but more accurate at distance. If you use the ACOG like a standard scope (one eye closed,) it will work like a standard scope, providing crisp, clear images.
Hopefully I've explained the BAC clearly enough........ [:)]