Splitting of atomic energy levels into a larger number of levels when magnetic fields are present; the resulting spectral lines are also split. The pattern and amount of splitting indicate the strength of the magnetic field. Splitting is associated with the orbital angular momentum quantum number, l, of the atomic level, which can take non-negative integer values. The number of split levels in a magnetic field is 2 x l + 1. The spectroscopic notation used of chemists uses letters for l: s = 0, p = 1, d = 3, etc.
Splitting of spectral lines in sodium. Image source: http://www.homepages.ucl.ac.uk/~ucapphj/SodiumZeemanEffect.gif.