Named after Charles Messier - French astronomer (1730-1817).
Messier is a young lunar impact crater located on the Mare Fecunditatis. The crater has a discernible oblong shape that is not caused by foreshortening. The longer dimension is oriented in an east–west direction. Just to the west lies Messier A, a similar-sized crater with an oblong, doublet form. (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.