Spin is a fundamental degree of freedom in a particle. You can ask where a particle is moving. You can ask what its momentum is. You can ask its spin along an axis.
Experimentally, spin is related to magnetism. If you shoot a beam of electrons through a non-uniform magnetic field, you'll see that the beam splits into exactly two beams.
Classically, it was reasoned that this phenomenon is due to electrons rotating about their own axis. Thus, it's called "spin".
Spin is also the same phenomenon that causes polarization in light.
Spin is a quantum property, so it's kinda funny. A fun little experiment (and the one I remember most vividly from high school physics) is this:
Take two photographic filters (
http://en.wikipedia.org/wiki/Photographic_filter).
Hold the first up to your eye. Put the second one in back of it and slowly rotate it.
The amount of light that goes through depends on the rotation. If the filters are aligned properly, 50% of the light goes through. If you rotate it 90º, suddenly, the filters block 100% of the light. Rotate it another 90º, and you're back to 50%.
Here's the weird part. Rotate them so that all the light is blocked. Now take a third filter at a 45º angle to the others. Put it in between. What happens?
(Well, if you filter out ALL the light, then filter out some MORE, you've stilled filtered out ALL the light... right?)
The amazing thing is that by adding that third filter, suddenly, light gets through again!
