The reactivity of elements is described by the tendency to attain noble gas configuration (to attain a completely filled outer shell).
Carbon has 4 electrons in its outermost shell. So to attain completely filled outer shell, it can choose to accept 4 additional electrons or lose the 4 valence electrons to have noble gas configuration, but this is extremely difficult as the above mentioned processes are energetically unfavourable.
To overcome the above issue(s), the valence electrons are shared with other atoms and these shared electrons belong to outer shells of both atoms. The bond so formed by sharing the valence electrons is called covalent bonding. This way both atoms form a molecule and attain noble gas configuration.
