It's just a method for adding water flow in the tank, using a pump located outside the tank. You pull water directly from the display tank (or overflow box) and just pump it back into the tank through any sort of useful outlet. The water does not flow freely into a sump or other holding tank, just from the display, through the pump, and back to the display.
A closed-loop system normally employs a much larger pump. So, for example, you might have a 2000 gph pump that would drive a closed loop system or sea swirls and then not have any powerheads in the tank.
The advantage here is that you don't have ugly powerheads in the tank, and their associated heat load. Also, you would only have to do maintenance on the one pump instead of the half-dozen powerheads.