To ensure that a screw sits below the surface a tapered recess ( a countersink ), the same size as the screw head is made that allows the screw head to sit down into it.
When surfaces are fixed with screws that aren’t to show, the countersink goes down into the material, so that the screw is fixed well below the surface and far enough in, that the hole above the screw can be ‘plugged’ with a core of matching material. This is the case for wood plank flooring as many are screwed and plugged in preference to traditional nailing, and for cupboard side panels where the panel fits the frame, and for stone work.
The best workmanship shows the grain of the plugs as closely matched to the grain of the material as possible…. but that’s quite a job, and usually the closest match of colour and grain is acceptable.
Or the space above the screw head countersink is plugged with some sort of filler relevant to the surrounding surface, in order to provide a smooth plane for other decoration.
Sometimes the filler or plug can annoyingly ‘pop’ so that it stands proud of the surrounding surface, and the only way to deal with it is to sand it off or to cut out and re-fill or re-plug. If it happens again in a place that matters, take out the covering and change the screw(s). This seems to happen most often with built in cupboards, especially when the materials aren’t wood – so as it’s not an attractive look, it’s not a bad idea to wait a year or so to allow the whole thing to move and adapt as it will to the given conditions, before any fine decoration or sensitive wallpapering is carried out.
The conical cutter that is used to make the hole is also called a countersink.
See also counterbore