In quantum mechanics, the spin of a particle or collection of particles is quantized. In particular, all particles have either half integer or integer spin. In the most general case, the eigenspinors for a system can be quite complicated. If you have a collection of the Avogadro number of particles, each one with two (or more) possible spin states, writing down a complete set of eigenspinors would not be practically possible. However, eigenspinors are very useful when dealing with the spins of a very small number of particles.