L-S coupling

When we try to combine quantum mechanics with relativity, in the case of Fermions (as in the Dirac equation), conservation of angular momentum requires the introduction of an extra angular momentum which has no analog in classical mechanics. This is called the spin. In the case of the electron, this angular momentum (magnitude) is expressible through the quantum number 1/2. Since the electron is charged, there is also a magnetic moment associated with the spin.
Note: Do not try to imagine the spin as a kind of spinning motion of the particle. This is a purely quantum-mechanical phenomenon and any classical analogy is bound to be wrong.

From the point of view of the electron, the nucleus is a positive charge going around it (due to the orbital motion of the electron). This creates a current loop which produces a magnetic field at the site of the electron. The magnetic moment of the electron due to the spin interacts with this magnetic field to cause small changes in energy.