If Craster has a daughter, once she grows up he marries her. However if the newborn is a boy he sacrifices the child to the Others when the white cold comes, in order to appease them. Of late the white cold has been coming more often.
A Clash of Kings
A Storm of Swords
During the mutiny at Craster's Keep, one of Craster's wives warns Samwell Tarly that Craster's sons will soon arrive for Gilly's newborn. Sam and Gilly manage to escape with the baby boy and make it to Castle Black
Game of Thrones
In the episode "Oathkeeper" the fate of Craster's sons is revealed when a White Walker riding an undead horse takes the last son of Craster and carries him towards a shattered mountain in the Lands of Always Winter.
Once inside, the White Walker approaches an icy altar ringed by large icy spikes and places the baby upon the altar. In the distance, a group of thirteen black-garbed White Walkers are revealed to be viewing the proceedings from afar. One of them breaks from the middle of their number and approaches the altar, stopping to regard the human child for a moment before gently gathering him in its arms. The baby immediately calms, staring into the face of the White Walker. It places its index finger upon the baby's cheek, causing the child's eyes to slow turn to icy, depthless blue and his skin to grow pale, transforming him into another White Walker.
In the novels as of A Dance with Dragons, there has been no evidence so far on what actually happens to the babies, though Craster's wives believe that the baby boys given by Craster to the Others are, in turn, transformed into new Others. Old Nan's tale's simply state that the Others feed human children to the wights.