Saturn's most prominent gap arises from a 2:1 mean-motion resonance with Mimas: ring particles there complete exactly two orbits for every one of Mimas's, receiving repeated gravitational kicks that clear the region.
Small moons orbiting just inside and outside a ring edge exert competing gravitational tugs that confine particles, preventing the ring from spreading by viscous diffusion. Prometheus and Pandora shepherd Saturn's F ring.
Inner particles orbit faster than outer ones. This differential rotation creates shear, stretching any radial structure into spiral density waves that propagate outward from resonance locations.
Saturn's rings may be geologically young — as little as 100 Myr old — possibly formed by tidal disruption of a moon or captured comet. Cassini data showed active mass loss; the rings may vanish in ~100 Myr.