Carrots support normal vision because of vitamin A, but won't give you night vision — that story was WWII propaganda.
Evidence & sources
Carrots supply beta-carotene, which the body can convert into vitamin A. Evidence: established. Known: Provitamin A carotenoids are well characterized. Unknown: Conversion efficiency differs between people. Source: NIH Office of Dietary Supplements, Vitamin A and Carotenoids Fact Sheet (Current revision).