Claws, along with fangs, are one of the first shifts in morphology to take place when a werewolf shapeshifts.
The fingernails thicken and become hooked and pointed. The claws can become detached from the werewolf, as in Lunatic one of Scott's claws became lodged in Jackson's car (though they can apparently grow back in later transformations) and a particular set of claws from Talia Hale were stored in the Triskele urn after her death.
A werewolf's claws are their primary instinctive offensive tools, like how fists are for human beings. Alphas, using their claws, can hinder the healing factor of other beings.
An Alpha's claws can also be used to transform a human into a were-creature with a scratch, similar to the Bite, though it is less effective.
Werewolf claws are also used in the process of mind melding.