Other forms: demurest; demurer
A demure person can be described as polite and a little shy. A demure outfit is a modest one — think high neckline and low hem.
Demure is a word you don't hear a lot these days, but it used to be a huge compliment for a woman or a girl, for them to be considered shy and quiet and modest. The word demure comes from an French term that means "sober, grave, or serious."