Named after Joahnnes Andreas Grib Fibiger - Danish pathologist, Nobel Prize winner 1926 (1867-1928).
Fibiger is a lunar impact crater located on the lunar near side near the northern pole. The nearest major feature is the Byrd crater. Located just North are craters Erlanger and Peary, which are 9.9 km and 73 km in diameter, respectively. (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.