Now that we have discussed hybrid orbital theory and resonance theory, let’s finally turn our attention to molecular orbital (MO) theory.  The power of the MO theory is not in visualizing the molecule and its bonds, but in the ability to predict whether a molecule will exist and explain its characteristics.
For every combination of atomic orbitals, there are two possible molecular orbitals, bonding and anti-bonding.  The term anti-bonding merely means it is a higher energy possibility, not that it does not participate in bonding.
For example, the two 1s orbitals in hydrogen can form two molecular orbitals. The plus and minus do not signify charge, but a favorable combination vs. a less favorable one. There is also an interactive multimedia animation (see screenshot above) in the Physical Chemistry book that shows the difference between VB and MO for hydrogen.

 
The two atomic orbitals create two molecular orbitals, a lower energy bonding orbital, and a higher energy anti-bonding orbital, designated with an asterisk (*).

Unlike Valence Bond (VB) theory, MO theory is only concerned with the orbitals of the possible molecule, individual electrons then fill the molecular orbitals (similar to filling electron configuration diagrams). The lowest energy MO is designated as a sigma bond orbital. VB and MO theories agree that a strong, stable sigma bond must be created first before creating pi bonds.
A possible arrangement of molecular orbitals created by the 2p orbitals is given below. Notice that unlike VB theory that requires electrons to be paired, MO theory requires them to fill the orbitals individually and results in two unpaired electrons for the oxygen molecule. This approach allows MO theory to predict the magnetic properties of oxygen where VB theory can not.

MO theory also helps predict the type of bond that will exist in a molecule using a calculation called the bond order (BO).  The bond order of a molecule is calculated by adding up the number of electrons in any bonding molecular orbitals and subtracting the number of electrons in any anti-bonding orbitals and dividing by two.
For the oxygen molecule, the bond order would be (6 – 2)/2 = 2 which indicates a double bond. A whole integer bond order indicates a highly favorable arrangement with a bond order of zero being very unfavorable.
The above is a very simplified look at MO diagrams and only a very brief explanation of their use. They become very complicated quickly and require the use of advanced computing technology but provide a wealth of knowledge for those that know how to interpret it. This is the reason that it is often only introduced in general chemistry but not used until higher level classes.
In summary, valence bond theory relies on the overlap of atomic orbitals with electrons in pairs. While it can help predict some characteristics, it is very useful in visualizing molecular shape. Molecular orbital theory is mostly concerned with the orbitals inside the molecule and once they are defined, the electrons are added individually.
The power of the MO theory is that it not only helps explain molecular characteristics but can also predict them as well as helping predict the stability of molecules.