Saturn is considered one of the gas giants. It is primarily composed of light gases, most of which is hydrogen. This allows a complex weather system, despite the fact Saturn is so far from the sun with little incoming heat. One reason is Saturn rotates on its axis so fast. And, that rotation is differential rotation.
What is differential rotation? Differential rotation refers to the fact that Saturn does not rotate like a solid, but instead rotates at different angular speeds at different latitudes. This also happens on the Sun and Jupiter. Differential rotation allows twisting of its atmosphere as one moves away or towards the equator other than the twists caused by a great Coriolis effect, the tendency of moving air to deflect to the right in the northern atmosphere and to the left in the southern hemisphere.
So, what is the Coriolis effect? Air must go around the planet in a day. It has farther to go near the equator in a given time. This results in the planet outrunning air moving towards the equator and being outrun by air moving towards a pole, since the east-west air flow is matched to the speed the planet is moving at the latitude. Saturn’s size and speed of rotation make this a Coriolis effect that is much greater on Saturn than on Earth, and is the effect that has much to do with our weather.
The result of Saturn’s atmospheric movements is it, like Jupiter, has alternating bands of wind direction as one moves from pole to pole.
Deep inside Saturn is probably, due to pressure and temperature, liquid hydrogen, solid hydrogen, then a rocky core possibly as large as the Earth. The liquid hydrogen moves electrons captured from the sun over billions of years which causes Saturn to maintain a strong magnetic field.