Size
Saturn can fit nearly 100 Earths inside it due to its massive size. This gives it a greater gravitational pull overall.
More Moons
Saturn's massive gravitational pull keeps 31 moons in orbit, and each of those moons exerts its own gravity.
Dust Rings
When asteroids and other objects smash into the moons, some of the dust and debris remains in orbit, held in place by the gravity from the planet and the moons. These "dust rings" are also visible around Jupiter, Uranus and Neptune.
Ice Rings
A second type of ring around Saturn is made up largely of huge chunks of ice. These large frozen objects may be bits of old moons or simply space debris that was too large to be pulled all the way to Saturn's core.
Ringless Earth
Earth has no rings primarily because it is much smaller than Saturn and thus exerts less gravitational pull.