late 14c. (early 14c. as an Anglo-French surname), "calm, settled;" of persons, "sober, grave, serious," from an Anglo-French extended form of Old French meur "mature, fully grown, ripe," hence "discreet" (Modern French mûr), from Latin maturus "mature" (see mature (v.)). The de- in this word is of uncertain meaning and origin. Barnhart suggests the Anglo-French word is from Old French demore, past participle of demorer "to stay," and influenced by meur. Klein suggests Old French de (bon) murs "of good manners," from murs (Modern French moeurs).
Now usually meaning "affectedly decorous, reserved, or coy" (1690s). Related: Demurely; demureness.