Molecular orbital theory doesn’t deal with resonance, but it makes resonance more understandable.
Whenever you can draw two or more Lewis structures for a molecule, the actual structure is none of the structures but is a resonance hybrid of them all. For example, we say that the two resonance structures of ozone contribute to a resonance hybrid in which the π electrons are delocalized between all three O atoms. This makes the two O-O bonds half way between single and double bonds or 1.5 bonds.
Molecular Orbital theory starts by assuming that the three atomic p orbitals on the O atoms overlap to form three molecular π orbitals that extend over the whole molecule. We end up with two electrons in a bonding π orbital; two electrons in a nonbonding #π^n# orbital; and no electrons in an antibonding #π^✳# orbital.
Calculations show that the #π# bond order of each O-O bond is 0.5. When we add the underlying σ bond, the total O-O bond order is 1 + 0.5 = 1.5. Thus, Molecular Orbital theory explains resonance delocalization automatically as the natural state of the molecule.