For example, using the Aufbau principle, Hund's rule and the Pauli exclusion principle we would write the following electron configuration for carbon
This would create a Lewis structure with one side (of 4) of the carbon having a pair of electrons and two sides having a single electron
Covelent bonds can form when there are unpaired electrons. So our initial electron configuation for carbon would allow us to predict that the carbon would form just two covalent bonds.
The hybridization of carbon produces the following electron configuration #1s^2##2s^1##2p^3# (called #sp^3# hybridization)
This would create a Lewis structure with a single electron on each of the four sides of carbon, allowing it to form four covalent bonds.
This means that carbon atoms will be able to achieve the octet rule when they form four bonds.