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Yup, actually carrots are good source of beta-carotene / Vitamin A which is necessary for good eye health and vision. Obviously carrots aren't the only source though.

"Vitamin A has multiple functions: it is important for growth and development, for the maintenance of the immune system and good vision.[2] Vitamin A is needed by the retina of the eye in the form of retinal, which combines with protein opsin to form rhodopsin, the light-absorbing molecule[3] necessary for both low-light (scotopic vision) and color vision."

https://en.wikipedia.org/wiki/Vitamin_A

it's got a grain of truth to it, so it's a believable smokescreen

So getting sufficient vitamin A from carrots or other sources is instrumental in keeping your eyes healthy. That's not the same thing as saying that eating additional carrots will give you super-vision.