m_s, the spin quantum number, is connected to the angular momentum associated with electron spin. The electron has a spin quantum number s = 1/2, which produces a spin angular momentum given by:

S = [s (s + 1)]1/2

h 2p

The spin can have two different directions given by the two allowed values of m_s. m_s = +1/2 is often called "spin up", and m_s = -1/2 is "spin down".