From Old French meur (Modern French mûr) from Latin maturus. The "de-" is unexplained.
- Distinguish from pronunciation of demur
demure (comparative more demure, superlative most demure)
- Quiet, modest, reserved, sober, or serious.
- She is a demure young lady.
Derived terms 
demure (third-person singular simple present demures, present participle demuring, simple past and past participle demured)
- (obsolete) To look demurely.
- (Can we find and add a quotation of Shakespeare to this entry?)