Named after Grove Karl Gilbert - American geologist (1843-1918), William; English physician and physicist (1544-1603).
Gilbert is a large Martian crater located in the south of the planet in the area of Promethei Terra. It is one of several large craters in the heavily pock-marked upland region. It was named in 1973 in honour of American geologist Grove K. Gilbert. (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.