Named after Arthur Cayley - British astronomer, mathematician (1821-1895).
Cayley is a small lunar impact crater that is located in a lava-flooded region to the west of Mare Tranquillitatis. It lies to the northwest of the smaller crater De Morgan and the larger D'Arrest. West and slightly north is Whewell, a crater of about the same dimensions. To the north is a linear rille designated Rima Ariadaeus, which follows a course to the east-southeast. (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.