The vampire claw is one of the natural weapons of the vampire.
The vampire on the show had razor-sharp claws on the tips of each of his fingers. Each claw was as strong as steel & swung with the vampire's superhuman strength (vampire expert Scott Bowen described a well-fed, healthy vampire as being six times as strong as an elite human athlete).
The idea of a Vampire having claws most likely came from the fact that the nails of a dead body are pushed outwards by expanding gases inside the corpses. Since then vampires have been depicted with claws, though vary. Sometimes they are decorative only, some are very long, some are retractable or can turn humanlike when in public. The idea of a vampire being superhuman has existed for generations, but the superhuman speed and strength demonstrated on the show is more common today in modern vampires.
30 days of Night showed the strength of Vampires in many ways. The Vampires could easily maul someone to death in about 1-5 seconds. One Vampire penetrated the skull of another Vampire, destroying his brain. This shows that Vampires are defensivley similar to humans. The Vampires can also dent cars with their punches and might be able to break completely through eventually. Even when striking this hard surface, the Vampire's hand wasn't injured from the recoil.
To test the vampire's ability to quickly deliver a killing strike to the zombie's brain with his claws, the Deadliest Warrior crew constructed a pneumatic vampire arm rigged to strike a model zombie skull with its claws. To get the right amount of force for the strike, professional strongman Clay Edgin was brought in to give them a measurement of the kind of force a human can deal with one blow against a techscan pressure mat.
The readings for Clay's punch were then multiplied by six to get the striking force of the vampire's claw, which was then fed into their mechanical vampire arm. The arm struck the model zombie head with over 8 thousand pounds of force, piercing through to its brain in barely over 1 second.
The experts claim that the vampire's speed and strength are determined by their rich blood combined with a rapidly beating heart. When they lose blood, a vampire's strength and speed will drop.
The simulated scenes and fight showed other examples of the Vampire's strength. One scene had the vampire rip open a door from its hinges using only the tip of his fingers. In the fight, the Vampires were able to stomp some zombies to death with their legs. They could also lift and throw zombies with enough force to kill them, one able to flip about 4 zombies at once. Two vampires attempted to hold a door shut, but a zombie horde is easily able to outperform them in strength.