Gauss belongs to a category of lunar formations called a walled plain, meaning that it has a diameter of at least 110 kilometers, with a somewhat sunken floor and little or no central massif. To the northeast is Riemann, another walled plain that lies even closer to the limb. Southwest is the crater pair of Hahn and Berosus. (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.