Counterbore, or counterbore cutters, are drill-bits used to make counterbore holes, which is a way of creating a flat-bottomed extension of an existing hole in a material. The counterbore cutter will essentially create a cylindrical cavity at the head of an already drilled hole. This allows the hole to accommodate flat bottomed screw or bolts so that they sit flush to the surface of the material, rather than protruding, while still able to perform their function to the fullest.
The reasons for desiring a counterbore of sunken screw are many. There are aesthetic reasons a manufacturer may want to hide the fixings, in furniture for example, but there are also aerodynamic reasons that are applicable to the aerospace industry.
Counterbores will often be made to be slightly larger than an accommodating bolt, to allow the use of socket wrenches or even screw caps.