Covalent bonds are the strongest type of chemical bond and are created between atoms with similar electronegativity. In general, electronegativity increases toward the right of the periodic table and decreases down the table. Electronegativity is not an atomic property, but emerges when atoms interact with each other.
According to modern atomic theory, atoms have electrons circling them in shells called orbitals. Each orbital has a maximum number of electrons, and each atom "wants" to max out its electrons in each orbital. Noble gases are the most stable elements because their electron orbitals all carry the maximum number of electrons. They are incapable of forming covalent bonds.
When two or more atoms have similar electronegativity, conditions are ripe for covalent bonding. The electron orbitals of both atoms are seeking a similar number of other electrons to max out their electron shells. When the atoms are brought together, their electron shells intermingle, and create something called "molecular orbitals," where electrons wander freely between both atoms and orbit the nuclei of both. This makes covalently bonded materials, such as diamond and many metals, quite conductive. In contrast, ionic bonds, such as the type of bonds that hold together sodium chloride (salt), electrons keep to their respective atoms, and the overall molecular structure is weaker as a result.
Covalent bonds are not common within the processes of life because it takes too much energy to break them apart, making them too hard to work with. Depending on the number of shared electron pairs, the bond is characterized as single, double, triple, and so on. Some of the metals with the highest melting points, molybdenum and rhenium, have quadruple bonds. Quintuple and sextuple bonds are quite rare, and there is good reason to believe that nothing on the periodic table can go beyond a sextuple bond.