To chamfer or form a depression around the top of (a hole in wood, metal, etc.) for the reception of the head of a screw or bolt below the surface, either wholly or in part; as, to countersink a hole for a screw. [1913 Webster]
To cause to sink even with or below the surface; as, to countersink a screw or bolt into woodwork. [1913 Webster]

countersink, n.

An enlargement of the upper part of a hole, forming a cavity or depression for receiving the head of a screw or bolt. [1913 Webster]
" In the United States a flaring cavity formed by chamfering the edges of a round hole is called a countersink, while a cylindrical flat-bottomed enlargement of the mouth of the hole is usually called a conterbore." [1913 Webster]
A drill or cutting tool for countersinking holes. [1913 Webster]

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OXFORD DICTIONARY

countersink, v.tr. (past and past part. -sunk)
1 enlarge and bevel (the rim of a hole) so that a screw or bolt can be inserted flush with the surface.
2 sink (a screw etc.) in such a hole.

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