Classical picture: The magnetic spin is a measurable quantity representing the spin or kinetic momentum of the particle. The kinetic momentum is linked to the "spin velocity" of the particle.
More pragmatic picture:
The magnetic spin is a measurable quantity representing
one of the electromagnetic components of the particle interactions.
In the case of neutrino, the magnetic spin gives to it the possibility
to interact electro-magnetically with electrons.
If its magnetic spin is for instance 10-20 MeV/Tesla
and if its energy is about 2 MeV, then its probability to interact
electro-magnetically becomes of the same order of magnitude as its probability
to interact by weak interaction.