Takeoff is the phase of flight in which an aircraft goes through a transition from moving along the ground (taxiing) to flying in the air, usually starting on a runway. For balloons, helicopters and some specialized fixed-wing aircraft (VTOL aircraft such as the Harrier), no runway is needed.
A plane flies through the air by continually pushing and pulling the surrounding air downward. In response to the force of moving the air down, the air pushes the airplane upward. Newton's 3rd law of motion states that for every action there is an equal and opposite reaction.