Think of unpolarized light as the incoherent sum of two polarized beams, with orthogonal polarizations. When you polarize the light, you are letting through the beams with the one polarization and not the other, so you have half the energy getting through. The polarization of an electromagnetic wave is the electric field vector after the wave dependence has been factored out, different from the induced polarization of a material. The magnetic field vector is always there, but in free space it is trivially related to the electric field vector, so we ignore it.