Named after Of Halikarnassus Herodotus - Greek historian (c. 484-408 B.C.).
Herodotus is a lunar crater located on a low shelf in the midst of the Oceanus Procellarum. To the east is the slightly larger crater Aristarchus. West across the mare is Schiaparelli. Almost due south on the mare surface is a solitary lunar dome designated Herodotus Omega (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.