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.
early 14c., "quiet, modest, demure," from Old French coi, earlier quei "quiet, still, placid, gentle," ultimately from Latin quietus "free; calm, resting" (from PIE root *kweie- "to rest, be quiet"). Meaning "shy, bashful" emerged late 14c. Meaning "unwilling to commit" is by 1961. Related: Coyly; coyness.
1704, "woman who affects or upholds modesty in conduct and thought in a degree considered rigid and excessive," from French prude "excessively prim or demure woman," first recorded in Molière.
Perhaps it is a false back-formation or an ellipsis of preudefemme "a discreet, modest woman," from Old French prodefame "noblewoman, gentlewoman; wife, consort," the fem. equivalent of prudhomme "a brave man" (see proud (adj.)). Or perhaps the French noun is from the French adjective prude "prudish," from Old French prude, prode, preude, which however is attested only in a laudatory sense, "good, virtuous, modest," a feminine form of the adjective preux. Also occasionally as an adjective in English 18c.; the application of the noun to a man was still considered rare at the end of 19c.