Covalent bonds are chemical bonds where electrons are shared between two atoms. Covalent bonding forms molecules. It occurs when the difference of electronegativity between the two atoms is less than 1.67, except when a metallic bond is formed. If the difference is 1.67 or greater, then an ionic bond is formed. Covalent bonds are formed to let each atom have full outer electron configurations. This consists of typically 8 electrons in the outer electron configuration, however, a configuration of only two electrons also is chemically stable.
Covalently bonded molecules have (in general) low melting points, are in the forms of brittle solids or gases, and are easily dissolved in water, however, when they are dissolved, they do not typically conduct electricity. Covalent bonds are generally weaker than ionic bonds.
Covalent bonds formed between two atoms of the same element are said to be "perfectly covalent" because their electronegativity. This is most common in the seven elements that occur natrually in diatomic form: H, N, O, F, Cl, Br, and I. This causes the only truly nonpolar covalent molecules.