A countersunk hole is simply a normal right cylindrical through-hole with an additional right conical section removed on the top. The cone angle is typically 82 or 100 degrees.
Countersinking is creating a tapered hole drilled with a wide outer portion. This is done to allow the head of a countersunk bolt or screw to site square with its surroundings when placed in the hole.
.031 diameter to 1.25 diameter