mid-13c. (late 12c. as a surname), "rich cloth" (often, but not necessarily, bright red), from a shortened form of Old French escarlate "scarlet (color), top-quality fabric" (12c., Modern French écarlate), which, with Medieval Latin scarlatum "scarlet, cloth of scarlet," Italian scarlatto, Spanish escarlate often is said to be from a Middle Eastern source, but perhaps is rather from a Germanic source akin to Old High German scarlachen, scharlachen (c. 1200), from scar "sheared" + lachen "cloth."
In English it is attested as the name of a color, a highly chromatic and brilliant red, from late 14c. It was used as an adjective in reference to this color, or to gowns of this color, from c. 1300.
Scarlet Lady is Biblical (Isaiah i.18, Revelation xvii.1-5); she has been variously identified by commentators. Scarlet woman "notoriously immoral woman, prostitute" (by 1924) perhaps is from notion of "red with shame or indignation." Earlier it was used in the same sense as Scarlet Lady.
Scarlet fever is from 1670s, so called for its characteristic rash. It also was an old slang term for the condition of women irresistibly glamoured by men in uniform. Scarlet oak, a New World tree, is so called from 1590s. Scarlet letter in figurative use traces to Hawthorne's story (1850), a red cloth "A" which convicted adulterers were condemned to wear. German Scharlach, Dutch scharlaken show influence of words cognate with English lake (n.2).