Essentially, helicopters stay up for the same reason airplanes move forward through the air. A rotating propeller creates changes in air pressure, lowering it in some areas and raising it in others. Combined with a specially curved wing, the effect is known as lift, and its what pulls an airplane forward or allows helicopters to lift off the ground vertically. Without some sort of rotary propeller system, neither aircraft would ever leave the ground.
There are two basic types of aircraft, fixed-wing and rotary-wing. A traditional airplane would be considered a fixed-wing aircraft, because the wings are in a rigid position behind or over the propellers. Helicopters, on the other hand, are rotary-wing aircraft, because the wing-shaped rotor blades spin in a circle above the aircraft's body. The individual blades of a helicopter's rotor are adjustable during flight, while a fixed-wing aircraft's wings have very few moving parts.
The reason why helicopters stay up in the air is because the individual rotary blades are shaped like airplane wings. Once the spinning rotor assembly has reached a certain speed, the curved blades chop up the air around them, creating lower pressure above the blade and higher pressure below. This action creates a pushing or lifting force from below. The pilot uses hand and foot controls to change the angle of attack on each blade as they spin. This angle affects whether the helicopter will rise, descend, turn, or even hover.
When the blades are held level, the helicopter may remain in place or lift slightly. If the pilot lowers the back of the blades, the resulting change in lift will send the helicopter upwards, much like a kite will fly higher when angled against the wind. If the pilot raises the back edge of the blades, the helicopter will descend. By varying the position of each rotary blade, the helicopter will move to the left or right. As long as the rotor is spinning at a sufficient speed, a helicopter should remain in the air.
One major problem helicopter pilots face is the tendency of the helicopter to turn in the opposite direction of the rotary blades. A second rotary propeller placed in the rear of the helicopter helps to counteract this natural tendency by pushing against the spin. This second rotor also helps stabilize the helicopter during a difficult hovering maneuver. Without the aid of a rear rotor blade, helicopters would routinely spin out of control and crash.