Entry from Wikipedia, so take it with a grain of salt:
Wolverine's mutation also consists of animal-like adaptations of his body, including pronounced canines and three retractable claws housed within each forearm. While originally depicted as bionic implants created by the Weapon X program, the claws are later revealed to be a natural part of his body. The claws are not made of keratin, as claws tend to be in the animal kingdom, but extremely dense bone, and can cut substances as durable as most metals, wood, and some varieties of stone. They can also be used to block attacks or projectiles, as well as dig into surfaces allowing Wolverine to climb structures. Wolverine's hands do not have openings for the claws to move through: they cut through his flesh every time he extrudes them, with occasional references implying that he feels a moment of intense pain each and every time he does so.
Again, retcon in action.