Let's say that something does happen to Saturn. Maybe it does 'explode or something' (though we realize that is extremely unlikely). First we would need to say just how far away from the Earth it is.
For convenience, the distance from the Sun to the Earth is called: one Astronomical Unit (AU). Saturn is a further 9 AU away, or a total of about 10 AU from the Sun. If you consider that the Earth is at 93 million miles or 150 million kilometers from the Sun, Saturn is an *enormous distance away! Between the Earth and Saturn there is lots of space for Mars, the asteroid belt, and the biggest planet Jupiter.
So what is Saturn made of? Saturn is called a gas giant, but it is not entirely gaseous. It is thought that the interior of Saturn is similar to that of Jupiter, having a small rocky core surrounded by hydrogen and helium. If we pretend that it has disintegrated there would be *lots of gas and a small amount of rock. The total mass would be the same as an intact planet, so it is logical to assume that most of the disintegrated materials would continue to orbit the Sun in roughly the same orbit as the intact planet. If the disintegration was violent enough some of the rock might be ejected away from the other material. However, that wouldn't concern us because of the enormous distance from Earth, the small amount of rock, the dispersal being a possible 360 degrees in every direction, and the presence of Jupiter between us and Saturn.
It is fortunate for us that there is a planet in the Solar System the size of Jupiter. (It is 318 times bigger than Earth!) There is evidence that Jupiter has enough gravity to attract many of the space rocks and comets that get close to it. It has been called the Solar System's vacuum cleaner.
So we don't need to worry that the Earth might be affected in any way by anything that might happen to Saturn.