The case of a perforated or slit eyelid can be a case where an injury occurred, but it can also be a congenital defect, like palpebral coloboma whose source is a genetic defect. According to the Rambam, the cases of halazon and nahash are both situations of pterygium, a common hereditary condition where a membrane grows on the inner part of the eye and spreads to the pupil.
When the Torah discusses those mumim – blemishes – that will disqualify an animal from being brought as a sacrifice (Vayikra 22:21-24), among those blemishes are problems with the eye. When talking about blemishes that will preclude a kohen from performing the Temple service (Vayikra 21:18-21) the Torah specifies a number of eye conditions, like someone who is tevallul be-eino.
The Mishnah on today’s daf (=page) applies these to the case of a firstborn, teaching that “One whose eyelid is perforated, nipped or slit, or if it has a cataract or a tevallul, halazon (snail-shaped), nahash (snake-shaped) and a growth on the eye, is disqualified.”
The Mishnah asks:
“What does tevallul mean? The white of the eye breaking through the ring and encroaching on the black, but if the black breaks through the ring and invades the white, it is not a disqualifying blemish, because there are no disqualifying blemishes as regards the white of the eye.”
The black of the eye is the pupil, while the white of the eye is the sclera. Between these two is the iris, which serves to control the size and diameter of the pupil. The “blemishes” described by the Mishnah are well-known conditions. What the Mishnah calls the white of the eye encroaching on the black is a cyst of the iris, while the black invading the white is a coloboma of the iris.