Small pieces of rock inside Roche's Limit can't clump together to form larger bodies; they keep breaking apart. Since the rings are inside the Limit, small particles stay small and never clump together to form moons.
How the rings got there is a big mystery. There are several theories. According to one, all the particles of rock and ice were already there when the planet Saturn formed.
Another theory is that Saturn's gravity captured a giant comet or asteroid and caused it to break apart. The pieces might have formed the rings. Still another theory is that a meteorite smashed into a small moon, breaking both of them to pieces, which became the rings.