The knowledge that light is polarized precedes the knowledge of the existence of the photon, see polarization of light for the classical point of view.
The polarization state and how it can be decomposed into different modes can be well visualized with the Poincaré sphere.
One key idea about photon polarization is that it carries angular momentum. Therefore, when an electron changes orbitals in the Schrödinger equation solution for the hydrogen atom, the angular momentum (as well as energy) change is carried out by the polarization of the photon!