A "boost cutout" was more accurately a boost regulator cutout. The boost regulator was part of the linkage between the throttle lever and the actual throttle valve, and limited the throttle valve opening in order to avoid over-boosting the engine in normal operations. In an emergency the boost cutout lever could be pulled and an extra couple of pounds of boost gained.
It also slowly opened the throttle, without moving the throttle lever, as the aircraft climbed in order maintain the selected manifold air pressure until you reached full throttle height.
Of course the term may have found other meanings since then.
I've slowly come round to the conclusion that the Americans were right; manifold air pressure is a much more useful term than boost pressure.