My father wears an eyepatch since he developed a double vision problem last fall. He’s been told by an eye doctor that they can give him special refractive lenses to help resolve it, but for the present he finds that putting a patch over the weaker eye is more comfortable.
I can think of a couple reasons:
Cosmetic, if one eye is blind or missing an eyepatch can alleviate people staring at it.
I have amblyopia, specifically the lazy eye variety (also my left eye, the lazy one, seems to be far sighted while my right is near sighted) to help with eye correction I had to wear a patch on my glasses over my good eye to help my left eye get better when I was little.
Once during a horn flash in band I hit my head with my trombone and my left eye started twitching uncontrollably. The doctor couldn’t figure out what the hell happened (I didn’t hit it hard at all) and I just had to wear an eye patch over the eye to rest it until it calmed down and stopped twitching (it took two days).