If you just need a very simple visualization, picture a Mobius strip. You need to go two revolutions around it to end up where you started from. It works like that on many levels.
Notice that you can glue the strip with half-twist, full twist, twist-and-a-half, etc. Just like with spins, a strip with integer twist will get you back to the same exact spot after a 360° rotation. Half-integer will require a 720° turn.
But if you want to understand where all of this comes from and how it works, you need Quantum Mechanics, and I'm guessing, you don't have much of a background in that.