A nail is a horn-like envelope covering the dorsal aspect of the terminal phalanges of fingers and toes in humans, most non-human primate

Primate

A primate is a mammal of the order Primates , which contains prosimians and simians. Primates arose from ancestors that lived in the trees of tropical forests; many primate characteristics represent adaptations to life in this challenging three-dimensional environment...

s, and a few other mammal

Mammal

Mammals are members of a class of air-breathing vertebrate animals characterised by the possession of endothermy, hair, three middle ear bones, and mammary glands functional in mothers with young...

s. Nails are similar to claw

Claw

A claw is a curved, pointed appendage, found at the end of a toe or finger in most mammals, birds, and some reptiles. However, the word "claw" is also often used in reference to an invertebrate. Somewhat similar fine hooked structures are found in arthropods such as beetles and spiders, at the end...

s, which are found on numerous other animals.

Fingernails and toenails are made of a tough protein

Protein

Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

 called keratin

Keratin

Keratin refers to a family of fibrous structural proteins. Keratin is the key of structural material making up the outer layer of human skin. It is also the key structural component of hair and nails...

, as are animals' hooves and horns. The mammalian nail, claw, and hoof are all examples of unguis [plural ungues].
The nail consists of the nail plate, the nail matrix and the nail bed below it, and the grooves surrounding it.
The matrix (synonyms: matrix unguis, keratogenous membrane, nail matrix, onychostroma) is the tissue (or germinal

Germ layer

A germ layer, occasionally referred to as a germinal epithelium, is a group of cells, formed during animal embryogenesis. Germ layers are particularly pronounced in the vertebrates; however, all animals more complex than sponges produce two or three primary tissue layers...

 matrix

Matrix (biology)

In biology, matrix is the material between animal or plant cells, in which more specialized structures are embedded, and a specific part of the mitochondrion that is the site of oxidation of organic molecules. The internal structure of connective tissues is an extracellular matrix...

) upon which the nail rests, the part of the nail bed that extends beneath the nail root and contains nerves, lymph and blood vessels.
The matrix is responsible for the production of the cells that become the nail plate.