How did Nick Fury lose his eye and get his eye patch?
Fury's injured left eye, though initially minimally affected by a grenade blast during World War II, has over the decades resulted in a 95% loss of vision in this eye.
However, I doubt Nick Fury from the movie got it for the same reason, he probably did not participate to World War II and he was not in Captain America's frozen luggage.
Also, in several closeups, you can see black veins extending from his eye patch, and 3 parallel scars like he was scratched by claws.
If we include information from the comic books and other sources, what's the explanation for the loss of his eye and the scars around it we see in the movie?
I thought he did participate in WW2 - weren't he and Dum Dum Duggan and someone else part of Cap's team dealing with the Red Skull? hmmm... no, it looks like just Dum Dum and Gabe...
The one clue we have is that it seems to be the result of a betrayal: in *Captain America: The Winter Soldier*, Nick Fury tells Cap, "the last time I trusted someone, I lost an eye." No details on who that might be, but it's a notable clue.
Spolier for Captain Marvel (2019)
It’s Goose, the Cat/Flerken that scratches Fury right across the eye.
I believe Goose is simply a Flerken; it’s just that Flerkens, to the untrained eye, look very similar to earth’s domestic cat.
@PaulD.Waite Indeed, but Goose is first introduced as a cat, we only learn later that it's a Flerken.
Makes me wonder whether the claw scratches as shown in the question was foreshadowing that scene in Captain Marvel.
Nick Fury's background is unknown, at least in the Marvel Cinematic Universe. But we can find some answers from the comics.
Originally as treatment for a hand grenade injury (and now for old age) Earth 616 Nick Fury receives regular injections of the infinity formula. This slowed/stopped his aging, allowing him to serve well past the age of 100.
Ultimate Nick Fury, based on Samuel Jackson also received anti-aging treatment as part of Operation Rebirth, another part of the supersoldier Weapon Plus program that created Captain America and several other Marvel heroes. In this timeline he also has increased strength and agility, though far from Cap's.
Anti-aging is a core aspect of Fury's character in two major universes. It seems likely it's also the case in the films. He probably still got it in World War II.
In the Ultimate Universe, he got it in a roadside bombing, where Weapon X (the future Wolverine) escaped his adamantium cage (bent, not broken). Logan killed everyone except Fury (the Allied forces were largely already dead), and carried Fury back to friendly lines. It was later revealed that this was a result of them having served in WWII together, during which Logan became the first mutant and Fury was a test subject for the first attempted recreation of the super soldier serum.
In the cartoon series Nick Fury got into a fight with the Grim Reaper and was slashed by the scythe therefore he lost sight and cheated death which is why through the movie when Nick gets hurt those veins protrude and are black.
Also in the Avengers cartoon series after his fight with the reaper Nick's hair goes a bit grey symbolizing death. This may not be correct but I am very observant and this is my conclusion on why Nick Fury has an eye-patch and whatnot.