spin, in this case, refers to how the particle is thought to rotate. The actual thing is that there is a field that the particle produces, and that field is thought (in our mental models of why there is a field) to involve a rotation.
In simple mental image terms, it is exactly the same thing as how the earth "spins", except at a much greater rate, of course. The earth could spin in the opposite direction, naturally. Well, so can any particle.
It is something of the nature of the fields that two identical objects cannot occupy the same "location" and possess the same "spin".
We cannot actually and truly see the spin, but that is how we imagine the thing acting because of the effects that we can observe.