What is hybridisation?

Hybridisation is a chemical phenomenon that occurs in certain atoms, whereby atomic orbitals 'mix' or 'hybridise' from their usual arrangement to form a more energetically-favourable orbital arrangement. Consider the molecule Methane (CH₄); in this molecule, the central carbon atom forms equivalent covalent bonds with 4 hydrogen atoms. However, the outer energy level of carbon shows that there are two electrons contained in the 2S orbital, and two electrons contained in the 2P orbital. These P orbitals are of higher energy than the S orbitals, so carbons orbital arrangement must change in order to form the 4 equivalent covalent bonds. This is where hybridisation comes in: an electron is promoted from the 2S orbital into the unoccupied 2Pz orbital, and then hybridisation of the second energy level occurs. This means that the 2S orbital now containing only one electron mixes with the three 2P orbitals, each containing one electron, to form 4 new "SP3" hybrid orbitals. These orbitals are all of equal energy, which is slightly lower than that of the 2P orbitals, which means that it is energetically favourable for carbon to hybridise in methane. This explains how it can form 4 equivalent covalent bonds in methane! (An energy level diagram of the orbitals would also be useful to explain, but I a, not sure how to draw one here).