Degenerate orbitals are orbitals in a quantum system that have the same energies.
In molecular orbital theory, molecular systems usually consist of many electrons capable of occupying two spectroscopic families of orbitals: valence-shell or frontier and inner or core-level. The number of valence-shell or frontier electrons is typically larger than the number for inner or core level electrons meaning it will be easier to find two different states with the same energy for valenceshells (degenerate) compared to finding a state in each atomic orbital (non degenerate). This becomes very important when an electron enters a molecular orbital containing other well occupied/overwhelmed charge density, as the probability distribution functions overlap more often leading to the electron having a higher chance of finding two states with similar energies (degenerate) compared to finding one state in each atomic orbital (non degenerate).
Degenerate orbitals are also known as stabilised orbitals because if they have similar energies then any change in the electron’s energy (e.g. as a result of an external perturbation) will not be able to change the orbital, meaning that the electron will more likely to move back to the orbital it had originally occupied.