Named after Anaximenes - Greek astronomer (585-528 B.C.).
Anaximenes is a low-rimmed lunar crater that is located near the north-northwest limb. It lies to the west of the crater Philolaus, and northeast of Carpenter. To the northwest is Poncelet, close to the visible edge. The outer rim has been eroded and worn into a roughly circular ring of ridges. (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.