countersink

Short definition from Wiktionary

Noun

1. 1
   A conical recess, typically machined at the mouth of a hole to admit a screw (with a matching taper) so that the screw sits flush with a surface.
2. 2
   The cutter used to cut such a recess. (Also used, at less depth, for edge-breaking/deburring.)

Verb

1. 1
   To create such a conical recess.
2. 2
   To cause to sink even with or below the surface.