1st consider the bonding in methane, CH4. The carbon atom forms 4 single covalent bonds to hydrogen atoms. However, when we consider the electronic configuration of Carbon (electrons-in-box notation), there are only 2 unpaired valence electrons, and hence there are only 2 available electrons for bonding. Hybridization is the process by which 4 electrons are made available for bonding.
Consider the energy profile diagram of the Carbon atom. The 1st step in hybridisation is the promotion of one electron from the filled 2s orbital to the empty 2pz orbital. Now all the 2s and 2p orbitals are singly occupied. The 2nd step is the rearrangement of these orbitals into 4 degenerate sp3 hybrid orbitals. The reason for hybridisation is found in comparing the energy released when 2 bonds are formed versus when 4 bonds are formed. Twice as much energy is capable of being released when Carbon is hybridised than when it is not. Therefore, Carbon is in a more stable and lower-energy state when hybridised.