The resonances are not that strange. Think of a ring particle orbiting. It will be perturbed by the weak gravity from a moon, occasionally dragged outwards, occasionally dragged inwards. In some places this averages out to zero: the particle and the moon have orbits that are so different that the total effect is random. But imagine that the particle has a period exactly half of the moon: every other time the particle is in a certain place the moon will be outside there too, perturbing it. The result is that the attraction adds up, and the particle goes somewhere else. The result is an empty gap in the ring wherever particles find themselves in a resonance with a moon. In other places you get a reverse effect that thickens the particles. Mathematically, you get gaps where the periods of ring particles is some simple integer ratio p/q of a moon period: the big Cassini division is due to the presence of Mimas. Some gaps are due to small moonlets inside the rings who have a 1/1 resonance (like Pan in the Encke gap). The same thing happens in the asteroid belt with Jupiter, but these gaps (the Kirkwood gaps) are less obvious since the asteroids have so eccentric orbits and with big inclinations. Saturn's ring particles move almost perfectly circularly in a plane.