I must stress that the idea of an electron spinning isn't quite accurate. Electrons have wave properties too and we don't really associate waves as spinning, do we? It is true, however, that the "electron spin" is related to its angular momentum.
Don't mean to nit pick, but think about the context too. this is a chem board and even though NMR uses physical properties not chemical properties for its analysis, wave particle duality is not essential to analysis.
For anyone reading this who doesn't do physics and is thinking what the hell is going on, in essence hydrogen protons align themselves to the powerful external magnetic field, somewhat akin to tiny magnets. However, they can align with or against the field. As the sample is rotated in the field, the hydrogen protons switch alignment, oscillating with then against the magnetic field. The frequency of oscillation (measured as chemical shift) can vary due to electron shielding or strong electronegative element nearby eg oxygen. Neighbouring Hydrogen atoms have a similar effect, but instead of shifting the entire peak like say an oxygen atom in a hydroxyl bond does, it causes variations in chemical shift.
btw carbon 13 NMR is a different theory altogether from 1-hydrogen NMR so don't get me started on that too haha
EDIT: sorry, was in a rush when I typed this so a few of the terms were incorrect. hopefully didn't confuse anyone