I understand that the square of the wave function is the probability density of finding an electron. However, what is the wave function itself? I am trying to understand molecular orbital theory but this concept is getting in the way of me completely understanding it. Any help would be great. Thanks.
It is often asked "what is waving when a particle is described as a wave?" and the correct response is "existence itself is waving."
The wavefunction is most elegantly described as a description of reality for your system. You then act on the wavefuntion with a hamiltonian to yeild an eigenvalue to quantify the energy.