The spin of a particle is a fundamental particle property that can be treated mathematically like an angular momentum.
Different particles can be assigned different spin values s. For example, electrons, protons, and neutrons (all s=½) are called spin-½ particles, whereas a deuteron, a particle composed of proton and neutron, (s=1) we speak of a spin-1 particle. In nuclei, instead of s, one often speaks of the nuclear spin I.
Each spin-afflicted particle may occupy different energy levels associated with the orientation of the spin with respect to a preferred direction sz, most often the direction of the external magnetic field. In general, a particle can take 2s+1 orientations and thus occupy the same number of energy levels.
For example, this results in two possible orientations or energy levels for a proton, as illustrated in the graph above. As you can see, the distance between the energy levels increases with increasing magnetic field strength, which is still important for the later analysis of the polarization.