For a spin-1/2 system, the 1/2 refers to the quantum number s. Spin is spin angular momentum and is related to the intrinsic magnetic moment of a particle. Unlike orbital angular momentum (l = 0, 1, 2,...), spin angular momentum can take on integer and half-integer values (s = 0, 1/2, 1, 3/2, 2,...). Half-integer particles are called fermions (obeying Fermi-Dirac statistics) and integer spin particles are called bosons (obeying Bose-Einstein statistics).
The spin operators, Sx, Sy, and Sz represent the effect of a measurement of the spin in one of those three directions, while S2 describes the measurement of the spin squared of a particle. It turns out that these four operators can be written in terms of Pauli 2 x 2 matrices
as Si = ħ/2 σi, where specifically
The spin operators also obey the following commutation relations
and [Si, S2] = 0, based on the commutation relations of the Pauli matrices.