© Charles Chandler
Here is the "explanation" of Saturn's rings to be found in
Wikipedia:
There are two main theories regarding the origin of Saturn's rings. One theory, originally proposed by Édouard Roche in the 19th century, is that the rings were once a moon of Saturn (named Veritas, a Roman goddess who hid in a well) whose orbit decayed until it came close enough to be ripped apart by tidal forces. A variation of this theory is that the moon disintegrated after being struck by a large comet or asteroid. The second theory is that the rings were never part of a moon, but are instead left over from the original nebular material from which Saturn formed.
It seems likely however that they are composed of debris from the disruption of a moon 400 to 600 km in diameter, bigger than Mimas. The last time there were collisions large enough to be likely to disrupt a moon that large was during the Late Heavy Bombardment some four billion years ago.
Both "theories" of the formation of the rings address the source of the material, but not the form. The rings extend up to 80,000 km above Saturn's surface, with an estimated local thickness of as little as 10 meters. It obviously took a force to organize that much matter into a near infinitesimal plane. The two fundamental forces operative at this scale are gravity and electromagnetism. As gravity cannot organize matter into a plane, the only candidate is some configuration of EM forces.
Saturn's magnetic field is very simple — it's a solenoid that is axisymmetric to a high degree of accuracy.
1 We also know that magnetically-responsive matter (such as the diamagnetic ice crystals in the rings) can only be accelerated where the lines of magnetic force are converging, and the acceleration is only in the direction of the convergence. Hence in a solenoidal field, there will be magnetic acceleration toward the poles,
except on the equatorial plane. Thus the simplest explanation is that the rings represent just a slice of the entire debris field that once completely surrounded the planet, while magnetic acceleration eventually pulled all of the debris into Saturn via the poles, leaving just the equatorial plane.
2