If you're new to the thread, please don't post the Mythbusters episode again. Mythbusters is entertaining but it's not history (or more specifically, it's not historical proof of anything.)

I've answered this before. Patched together from a couple of answers in this thread:

Treasure Island gives us the "pirate" myth and attributes we see today -- eyepatches, cocked hats, parrots, wooden legs -- that sort of thing. Peter Pan has the pirate with a hook for a hand. Pirates of the Caribbean, the theme park exhibit, borrows from those and then spawns Pirates of the Caribbean, a movie franchise that spreads it, and so forth.

As to why pirates (sailors, etc) would wear eye patches, there's no particular nautical disease that would lead to that; it would be used to cover an empty eye socket or a blind eye. It's become associated with pirates through pop culture, which has treated pirates as a caricature of sailing men of the era. In much the same way, wooden legs or hooks for hands weren't unknown among sailors of the era, and seamen traveling to tropical lands might adopt parrots or apes/monkeys/what have you, but that sort of thing is not nearly as common as the pirate stereotype would make them out to be.

This previous thread, from our FAQs, may be of interest: https://www.reddit.com/r/AskHistorians/comments/1ozk2d/how_accurate_is_the_media_portrayal_of_pirates/

Also, the aforementioned Mythbusters episode asserts that pirates wore eye patches to preserve night vision. But, pirates did not wear eye patches for night vision, not that we know of. /u/davidaop, our pirate expert, and I have both answered questions about this in the past. Unfortunately, because it's not a thing people did, there's not a canonical source saying that people didn't do it (if that makes sense); there's just an absence of evidence, into which void people throw half-baked conjecture. And Mythbusters.