The external layer of the electronic sheath (which is responsible for the formation of covalent bonds) contains certain numbers of electrons and free places. Regular covalent bonds can only be formed, when both participating atoms contribute one electron and one free place in their outer sheaths.
Carbon (C) atoms for example contain four electrons and four free places in their external layer they can form four covalent bonds. The noble gas neon (Ne) in contrast contains eight electrons in the external layer and no free places therefore no covalent bonds are possible.
Two electrons from the external layer without respective free places are called "free electron pair". They can only participate in covalent bonds, when the partner atoms contain two free places within their external layer.