If you look up things like the Stern-Gerlach experiment, you may find the term space quantization mentioned. It simply means that an external field can create a variety of different energy states out of what were previously states of the same energy. Typically one gets this with the angular momentum of charged particles, as this creates magnetic moments which interact with electric or magnetic fields. QM tells you the angular momenta cannot adopt any orientation they like with respect to such a field, only particular orientations, associated with particular energy levels. (Having said all this I find relatively few references to the term "space quantization" on the internet. It may be that it is a term that has fallen out of favour since the 1970s when I learnt all this stuff.) Since the spin quantum number of the electron is 1/2, its spin angular momentum, s, = h/2pi √(1/2.(1.2 + 1)), i.e. just like other forms of quantized angular momentum. However its allowed projections, m(s), along a z axis defined by an external field, are + 1/2 h/2pi or - 1/2 h/2pi. All I'm saying is the quantum number m(s) only has significance in the presence of a field felt by the electron in question, because it is a projection of s, in a direction in space. The Pauli principle says no two electrons in an atom can have the same set of quantum numbers and of course, in an atom, m(s) is one of these, because the orbital angular momentum of the electron in an atomic orbital creates such a field. So you get different energies depending on whether the spin is up or down with respect to the orbital angular momentum, hence doublets etc. I think I've got this right - but it was 40 years ago, I admit.