So, what really does spin mean. Many textbooks present spin as a spinning top. This really is not the case. If we did look at it as a spinning top, we would have infinitely many directions as the top spins. We know experimentally that an electron is quantized and gives us only two possible values for spin which we denote up and down. (explanation of experiment below) An electron in a magnetic field will experience a force. Spin is typically measured by observing the orientation of the electron magnetic moment in a magnetic field. It can be in the direction of the field (+1/2) or opposed to the field (-1/2).1 You could also look at spin as spin angular momentum. It has been observed that values of angular momentum are restricted to half integer multiples of h/2pi. Unlike a classical spinning object which derives angular momentum from rotation of their constituent parts, spin angular momentum is not associated with any rotating internal masses. The electron therefore, has only two spins we denote +1/2 and -1/2.
In the experiment below, it can be seen that silver electrons subjected to a polarized field oriented in the z direction will show 50% of electrons deflected in the +1/2 direction (up) and 50% in the -1/2 direction (down). As different parts are blocked and different axis orientations introduced, the spin behavior can be explained below.
When we look at electrons in a triplet state where both are electron are said to be oriented up (+1/2, +1/2), it gives an electronic spin quantum number of 1.
1. Miessler, G.L. and Tarr, D.A. (1999).
Chemistry, 2nd ed., Prentice Hall: New Jersey, p 23-25.