Named after David Brewster - Scottish optician (1781-1868).
Brewster is a small lunar impact crater in the northern fringes of Sinus Amoris. It lies to the southwest of the larger crater Römer. To the southeast is the similar-sized Franck. This crater is cup-shaped and symmetrical, with no overlapping craters of note. (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.