According to the search results, the White Walkers turn the babies into new White Walkers. They take the babies deep into the Lands of Always Winter to an altar hidden in the mountains, where the Night King approaches the baby and lays a finger across its cheek. At the Night Kings touch, the babys eyes turn the same shade of blue as the White Walkers, implying that this is how the icy creatures reproduce. The conversion of Crasters sons into baby White Walkers is the only way the Night King and his brood can procreate. It is also mentioned that infants are easier to mold into whatever the Night King wishes.