Countersunk magnet is an extremely popular neodymium magnet with countersunk/counterbore holes in the center. It is to allow the magnet to be easily fastened into place like woodwork for a temporary or permanent fitting. Besides reinforcement effect, bolt head will be inserted into counterbore with no influence on magnet appearance and external structure. It is great for many applications including manufacturing, woodworking (door/cabinet closures), art projects (hanging art/box on a wall) and many other custom applications.
A countersink is an angled taper applied to a hole that allows a fastener (usually a flat head screw or similar) to sit even with, or below the surface which has been countersunk. Countersinks can be measured by many different gauges. The easiest tool to use, assuming the tolerances aren't too tight, is a pocket comparator with a reticle. Optical comparators and CMMs are regularly used to measure countersinks with very tight tolerance.