common name of plants of the genus Daucus, cultivated from ancient times for their large, tapering, edible root, c. 1500, karette, from Middle French carrotte, from Latin carota, from Greek karoton "carrot," probably from PIE *kre-, from root *ker- (1) "horn; head," and so called for its horn-like shape. A Middle English name for the wild carrot was dauke (late 14c.), from Latin.
The plant originally was white-rooted and was a medicinal plant to the ancients, who used it as an aphrodisiac and to prevent poisoning. Not entirely distinguished from parsnips in ancient times. A purple-rooted variety existed perhaps as early as 7c. in Afghanistan and was introduced in Europe by Arabs c. 1100. It was cultivated into the modern orange root 16c.-17c. in the Netherlands. Thus the word's use as a color name is not recorded before 1670s in English, originally of yellowish-red hair.
The theory that carrots are good for the eyesight may have begun in ancient times, but it was "much embroidered in the Second World War, when, in order to encourage the consumption of carrots, one of the few foodstuffs not in short supply, the British authorities put it about that pilots of night-fighter aircraft consumed vast quantities to enable them to see in the dark." [Ayto, "Diner's Dictionary"]