The 1887 "Alligator Eye" Silver Dollar (VAM 12) is so-named because of the doubled cornea on Liberty's eye. This extra eyelid is known as a nictitating membrane and, in alligators, it serves as a shield for the eye and acts as a goggle when the alligator is underwater. Nictitating membranes are found in many animals, including fish, birds, amphibians, reptiles, and even some mammals (but not humans). Thus, this variety could just as easily have been called the Aardvark Variety or the Woodpecker Variety, had the namer been so inclined.
This variety is fairly common, with upwards of one thousand examples certified in Mint State.
1887 VAM 12 Alligator Eye Morgan Dollar