Claws are products of the skin, and are found at the tips of the digits of most four-legged animals. Claws consist of thick deposits of keratinized, flattened epithelial cells. Keratin is a fibrous protein that is also a major consistuent of hair, the outer layer of skin, reptile scales, and bird feathers.
A layer of cells called matrix cells, located at the base of the claw, produces new claw. The claw grows outward from the matrix, such that the newest claw cells are located at the base of the claw and the oldest cells at the tip.
Cross-section of a mammalian claw. The claw grows outward (blue arrows) from proliferating matrix cells at its base. Adapted from Kardong 1995.
Drawing from life of a side view (top) and bottom view (bottom) of a rat's claw.
The rat's claw has a sensitive pink "core" or "quick," called the nail bed, which you can see through the semi-transparent keratin. In humans, the nail bed is the flat pink part of the fingernail.
Claws are found in most four-legged animals. Primates have
flattened versions of these claws, called nails. In fact, primate
fingernails and toenails may actually be fetal versions of claws.
Anatomically, our unguis is flat and our subunguis is very reduced --
just a thin band of softer material under the outer edge of the nail.
Ungulates, like horses and cows, have an especially thick version of
the claw called a hoof.