To drill or enlarge a hole so that a screw head or bolt head sits flush with or below the surface.
From counter- + sink (from Old English sincan, to fall). A carpentry and mechanical term where 'counter' means opposite direction (outward enlargement) and 'sink' means to make go down.
Countersinking is invisible but essential—it's why aircraft fuselages are smooth rather than bumpy with screw heads, reducing drag and making them faster.
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