Named after James Cook - British explorer (1728-1779).
Cook is a lunar crater that lies in the western part of the Mare Fecunditatis, just to the southeast of the prominent crater Colombo. To the southwest is Monge. The interior of this crater has been flooded with lava, leaving only a low rim projecting above the surface. This rim is not quite circular, and has a somewhat hexagonal appearance. (wikipedia entry)
A crater is a circular depression likely created by an impact event. On the Moon they are named after deceased scientists, polar explorers, astronauts or cosmonauts.