Indeed it does...and its interpretation is not trivial at all. A short answer is the following; atomic orbitals have integer amounts of angular momentum, right? An s orbital has l = 0, a p orbital has l = 1, etc...what's more, if you put a 2p electron into a magnetic field, you see a separation of the states in energy; these correspond to the "magnetic" quantum number, m_l, having values 1, 0, -1... these numbers represent how much of the orbital momentum can be projected along the z axis; if m_l = 1, then the projection = +h; if m_l = -1, the projection = -h; if zero, the projection = 0.
As it happens, if you turn up the strength of the magnetic field, you start to see each of the m_l states split into two states; each of which corresponds to an electron having m_s = 1/2 or m_s = -1/2...thus, if m_s = 1/2 there is an additional component of angular momentum along the z axis = +h/2; if m_s = -1/2 there's an additional component = -h/2.
So, the electron behaves as if it has "built-in" angular momentum which can add to, or subtract from, the orbital angular momentum...and it adds/subtracts half as much angular momentum projection as orbital angular momentum does. Whew!! I hope that helped. Some short answer!!!