Hosel bore is the hollow for the shaft in the hosel part of a golf club head.
Its depth (called “hosel depth”, “hosel insertion depth” or “hosel bore depth”) is the distance from the hosel top to the bottom of the hosel bore.
Its inside diameter is called “hosel inside diameter” or “hosel bore diameter”. The diameter is expressed in thousandths of an inch. (e.g. 0.335″, 0.350″, 0.410″, 0.370″).