Named after Hippocrates - Greek doctor (c. 460-377 B.C.).
Hippocrates is a lunar crater on the far side. It is located in the northern region of the lunar surface, to the north of the crater Stebbins. To the southwest are Kirkwood and the large Sommerfeld. This is a old formation that has become worn and eroded due to subsequent impacts. (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.