You could crudely think of intrinsic spin as the particle spinning about its own axis. This was what physicists originally thought, and why it's called 'spin'.

You could crudely think of intrinsic spin as the particle spinning about its own axis. This was what physicists originally thought, and why it's called 'spin'. Though we've since learned this is not an accurate view. Otherwise you can think of spin as an angular momentum that's "just there", and restricted to a few quantized values. Electrons are spin-1/2 fermions, and their intrinsic-spin angular momentum can only have values of +/- hbar/2. Ie, in whatever direction you measure the electron's spin, you'll observe it either clockwise or counterclockwise around that axis, with value one-half hbar. Things get interesting in an atom, where the orbiting electron has an orbital angular momentum in addition to its spin angular momentum. And angular momenta interact in peculiar ways. (Link below). In a simple hydrogen you'll also have interactions between the spin of the single electron with the spin of the proton. In other atoms, say helium, there will be further interactions between the two electrons. https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_10.pdf https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-...