Counter-Bore refers to inserting a screw into a surface and ensuring that the head is not projecting outwards from the surface.  

In order to do this, buildings use screws through a whole that is 'Counter-Bored', which should be deep enough to prevent the screw head from protruding. The hole needs to have a flat bottomed cutter and may be plugged with the use of doweling to fully conceal the head of the screw.