Final answer:
The optic nerve is the structure that exits the back of the eye through the sclera, connecting the retina to the brain.
Step-by-step explanation:
The structure that exits the back of the eye, piercing through the sclera, is the optic nerve. It is responsible for transmitting visual information from the retina to the brain. Within the anatomy of the eye, the sclera is the white part and provides protective coverage for the eye, whereas the optic nerve connects the eye to the brain through the opening of the optic canal located at the posterior apex of the orbit.