Why are Saturns rings rings?

If there is enough orbiting material (as is the case with Saturn's rings), they will tend to form into a disk because of friction. There are less collisions if all the orbiting objects lie along the same plane, so that's how they end up given enough time. Imagine if there were some ring particles that did not orbit in the plane of saturn's rings. Twice every orbit they would pass through the rings, however, occasionally colliding with something. The colliding particles would tend to combine their angular velocities over time, bringing their orbital planes closer together. Eventually they would be the same.

Eel's got it right. But i would add one bit by analogy.

It works very similar to (but not exactly as) hand-tossing a pizza. when you start the pizza dough, it's an amorphous blob. But as you rotate it, you impart angular momentum, which drives the blob into a flat disc shape. Similar idea for Saturn's rings.

Also, many things in astronomy form discs and rings, such as galaxies, young stars, and planetary systems. This is for the exact same reason as Saturn (which, again, is slightly different than the pizza dough analogy).

Oh yeah, why the equator? Because the tangential velocity is the highest at the equator.