The eye that is damaged or lost from repeated prodding/poking, or Socket Rocketing.
Jake: Hey Zach, what happened to your eye?
Zach: My continued bad ideas led Paul to socket rocketing me repeatedly until my eye fell out. All I have now is this stupid eye patch.
Jake: Dude, that is one nasty Pirate's Eye
When a guy is getting a blow job and he misses his mark while cumming and it sprays across her upper lip and a little gets in her eye. She then yells "ARGH! ME' EYE!" while squinting the aforementioned eye closed, while the cum mustache drips down either side of her mouth, resembling a wickedpirate's facial hair.
I was giving my BF a hummer and he wanted to cum on my tits, but he misfired and I ended up with a Pirate 'Stache. My eye still stings and since then I keep getting whiffs of bleach.