late 14c., cressaunt, "crescent-shaped ornament," from Anglo-French cressaunt, from Old French creissant, croisant "crescent of the moon" (12c., Modern French croissant), from Latin crescentum (nominative crescens), present participle of crescere "come forth, spring up, grow, thrive, swell, increase in numbers or strength," from PIE root *ker- (2) "to grow."
Applied in Latin to the waxing moon, luna crescens, but subsequently in Latin mistaken to refer to the shape, not the stage. The original Latin sense is preserved in crescendo.
Meaning "moon's shape in its first or last quarter" is from mid-15c. in English. Meaning "small roll of bread made in the form of a crescent" is from 1886. Adjectival sense of "shaped like the crescent moon" is from c. 1600 (earlier it meant "increasing, growing," 1570s).
A badge or emblem of the Turkish sultans (probably chosen for its suggestion of "increase"); figurative sense of "Muslim political power" is from 1580s, but modern writers often falsely associate it with the Saracens of the Crusades or the Moors of Spain. Horns of the waxing moon are on the viewer's left side; those of the waning moon are on his right.