Ah, an astronomy question, my time to shine!
Saturn's rings are made up of rocks and dust, most of which are the size of a basketball or smaller. Some are the size of a car, some are the size of a house, and very few are the size of mountains. The rings themselves are less than a kilometer thick on average; they are VERY thin, thinner than a piece of paper a few hundred meters across. They are bright due to a large amount of water ice covering them; we as a species recently found out that this water ice is coming from one of the moons, Enceladus, that has a liquid water reserve under its surface. water ice is VERY reflective, and looks bright in sunlight. If you took all this material and crunched it into a ball, it would be a moon not much smaller than Mimas, aka the "Death Star" moon. Mimas is tiny, as an aside, Mimas is about as small as you can get and be round. Any smaller than Mimas, and you are not round any more, you start to look lumpy like a potato. So we are not talking about a lot of "stuff" here.
So, to explain this like I do to the kids at the telescopes, gravity is fascinating. If you are a moon, you are held together by (mostly) gravity. If you are a small moon orbiting a larger object, say a moon like Mimas orbiting Saturn, the big object tugs on you and creates tides. On earth we see these at the beach when the ocean rolls in. You also get tides in the rocks and metals of the earth, but they are way, way smaller and not noticeable unless you have sensitive equipment looking for that movement. If you as a moon get close enough to the big object, these tides can grow to be stronger than the gravity holding you together. The side of you close to the planet is being pulled harder than the rest of the moon facing the other way. This is called the Roche Limit. This limit for a body the size of Mimas, made out of mostly ice and rock is.... right where the rings are!
What we think happened is that a moon of Saturn got too close to the planet and ripped itself apart sometime in the distance past. Now, normally, a ring firms and the material either fades out into space, falls into the planet, or collides with itself and reforms a moon again. With Saturn, this did not happen.
And we get to talk about gravity for a second. Gravity, like I said, is fascinating. It is the weakest of the fundamental forces, yet can act over very long distances. Gravity loves to form resonances. A resonance, in the classic example used, is like the push of energy someone gives you on a swing to make you go higher and higher. Gravity can do the same thing with moons, stars, planets, even whole galaxies. Earth and Venus are in an almost resonance of 8:13 (every time the earth goes around the sun 8 times, Venus goes around the sun 13. This is a part of the basis for the Mayan calendar). Jupiter's big moons are in a 1:2:4 resonance that is very stable over long periods of time. Io goes around twice wile Europa goes around once; Europa goes around twice when Ganymede makes one full orbit. Back to Saturn, the moons closest to the rings, notably Enceladus and Mimas create stable zones where stuff can gather, and unstable zones where stuff will be kicked into a different orbit. The Cassini Division, which can be easily seen from earth, is the 2:1 resonance with Mimas. Anything that tries to orbit in this zone will eventually leave, creating a dimmer area that looks like a break in the ring.
Orbital Resonance article is here with a lot of math if I have made you curious.
The short answer for the kids is this: Saturn had a moon. It got too close and was pulled apart by Saturn's gravity. The remaining moons keep the dust and rocks in place for a long time!