Hi, there!
The term "spin" in quantum mechanics referes to the intrinsic angular momentum of a particle (which may be elementrary, liek electron or neutrino, or composed, like an atom or a golf ball). In this sense neutrino "spins" exactly like a spining golf ball.
There are elegant mathematical reasons [representation theory of SO(3) group] which imply that angular momentum of any isolated object is quantized -- that is, can assume only values that are multiples of hbar/2. For small objects (like elementary particles), the angular momentum is "small integer" * (1/2) * hbar, and angluar momentum quantization has pronounced effects.
For large objects the corresponding integer is HUGE and descrete effects of spin are unobservable.
Nothing misterious about spin!
