spin-½
A spin-½ particle is one whose intrinsic spin can give only two answers when measured along any chosen direction: a fixed amount up, or the same amount down. Electrons, protons, and neutrons are all spin-½, and so this simple two-outcome behaviour underlies most of ordinary matter. Whatever axis you pick, you always find one of just two results, never anything in between.
The label ½ refers to the spin quantum number s, which for these particles equals one half. The magnitude of the spin is set by s, but the part you measure along an axis comes in steps of the reduced Planck constant, here landing on plus or minus one half of it. Two outcomes is the smallest interesting case in quantum mechanics, which is why spin-½ is the model system for so much of the theory.
Precisely because it has only two states, spin-½ is the natural physical home of the quantum bit, or qubit. Anything that holds exactly two distinguishable quantum levels and can be placed in superpositions of them works the same way mathematically. Studying the electron's spin therefore teaches you the core arithmetic of quantum information at the same time.
Measure spin along any direction and you find plus or minus half of ħ — never anything between.
Two outcomes does not mean the spin only ever points two ways. It can be in a superposition pointing in any direction; the two values are just the possible results of a measurement along the axis you choose.