Mim is an adjective meaning 'affecting a shy or modest manner'; 'demure'; or 'affecting great moderation in eating and drinking'. It is most often applied to flirtatious females. While it does suggest that a person is 'acting' modest, it is not necessarily pejorative.
It first appeared in 1641, and stuck around for a few hundred years before fading to obscurity after the passage of the Victorian era. It may have arisen as an imitation of 'the act of pursing the lips'. It still makes an occasional appearance in modern literature.
On an unrelated note, mim- (also mimo-) is a prefix that arises from the word mime, meaning to mimic.