Craster's sons are the sons of the wildling Craster and his wives.
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
At Craster's Keep, one of Craster's wives called Gilly, who is visibly pregnant, tells Jon Snow that Craster gives up his infant sons to the cold gods; Jon determines she is speaking of the Others,
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.
If it's a girl, that's not so bad, she'll grown in a few years and he'll marry her. But Nella says its to be a boy, and she's had six and knows these things. He gives the boys to the gods. Come the white cold, he does and of late it comes more often. 
The boy's brothers…Craster's sons. The white cold's rising out there, crow. I can feel it in my bones. These poor old bones don't lie. They'll be here soon, the sons. —one of Craster's wives to Sam, after the mutiny
- ↑ A Storm of Swords, Chapter 33, Samwell II.
- ↑ 2.0 2.1 A Clash of Kings, Chapter 23, Jon III.