Babies who are born prematurely don't get the chance to finish all the growth processes that go into being a human. One such process occurs in the eyes. While in the womb, blood vessels grow until they reach the edge of the retina, but when a baby is born too early, the vessels haven't had time to reach their final destination. After the baby's born, those retinal edges send out distress signals to the rest of the eye, calling for nourishment. That causes the blood vessels to grow, but instead of growing normally, they grow every which way, a condition known as retinopathy of prematurity (ROP).
In some cases, this isn't a big deal, but in more severe cases, the blood vessels could cause leaking or bleeding in the eye. In the severest cases, they could cause the retina to detach from the back of the eye, resulting in blindness. The condition is only detectable through an eye exam, so you'll find lots of ophthalmologists roaming the halls of the NICU. The eye doctor will keep a watchful eye on the vessel growth to figure out if the baby will need laser surgery or cryotherapy to prevent long-term problems.