The simple answer is gravity. Imagine each of the particles that make up Saturn’s rings as moons in orbit around the gaseous body of the planet. Each of these particles is in freefall.
These particles often collide with one another and are affected by the gravity of their parent planet. A combination of collisions and other such forces mean that Saturn’s rings tend to spread out. Particles that are closer in to the planet can often be found falling into the planetary atmosphere.
Saturn’s ring system is quite intricate, with each ring being kept in place by the gravitational force of shepherd moons, which ‘herd’ each of the particles to keep them in shape.