Named after Aristillus - Greek astronomer (fl. c. 280 B.C.).
Aristillus is a prominent lunar impact crater that lies in the eastern Mare Imbrium. Directly to the south is the smaller crater Autolycus, while to the southwest is the large Archimedes. The area of mare to the southwest is named the Sinus Lunicus. To the northeast are the craters Theaetetus and Cassini. (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.