Because of the huge forces exerted on an F1 car, it can be incredibly difficult to turn the wheel without any assistance. Hydraulics are used to help ease this. Hydraulics are also used in other elements of the car such as the fuel-filler cap and the gearshift. Hydraulics are used over electronic systems because they are lighter.
The point of hydraulic fluid is to create a link between two points. Fluid cannot be compressed, whereas air can be. This means that by having a tube filled with liquid (hydraulic fluid), you will get an instant response when you press a button or pedal. This makes system control quicker and more consistent. An F1 car can experience a range of temperatures. Because of this, the hydraulic fluid is made to ensure that it will operate safely at a range of temperatures.