bull's-eye \bulz eye\ (noun) - 1 : The center of a target. 2 : A direct hit. 3 : A convex lens or a lantern with such a lens in it.
"While Greg was consistently able to hit the target's bull's-eye with his own pistol, he was off by several inches when using any other."
Why bull's eye? Why not a cat's eye or a dog's eye? Nobody knows. Perhaps it's an indication of the earlier agro-economy and the importance of bovine animals in it. It was probably suggested by the similarity of a bull's round eye with that of a target.