While doing some calculation in Statistical Mechanics of blackbody radiation from Huang's Statistical mechanics, I came across with the factor 2 which it says comes from two possible polarizations. Now, what does that essentially means?
The light coming off a black body will be randomly polarized, and this extra randomness allows more entropy in the photons, and thus more photons flying around in thermal equilibrium.
Why the 2? It's like spin. A spinning top in classical physics can take on any axis of spin. However, for electrons we are restricted to "spin up" and "spin down". After choosing a basis, the electrons spin state is described as that of a qubit. Mathematically, the state can take an infinite number of values, but this can't be used to store an arbitrarily large amount of information.
The state tells us the probabilities of measuring a 0 vs a 1 in our basis. If we could take many measurements, we could get a good estimate of these probabilities and the underlying state (there are ways of getting phase information as well). But we only get to make a single measurement, since doing so disrupts it. Qubits can only store two bits each (they get an extra bit from entanglement, see super dense coding, but that is beside the point), even though the mathematics allows them to take on any state.
The same happens for polarization. A light beam can have any arbitrary polarization angle. However, per photon there are only two polarizations "available" for entropy in the same sense that there are only two spins "available" for electrons.