Multicopters fly by utilizing two basic principles: lift and torque. Multicopters are truly a great exercise in Newtonian Physics (every action has an equal and opposite reaction). In a traditional helicopter, the main rotor spins in one direction. To keep the body from spinning the other way (remember, every action has an equal and opposite reaction), a tail rotor is implemented in order to put a constant pressure on the tail to keep the body stable. A multicopter uses counter-rotating propellers to keep the body stable while the propellers turn.
The axes of rotation on an aircraft are called pitch, yaw, and roll. Pitch is simply pointing the nose of the aircraft up or down. Yaw is turning the aircraft to the left or right. Roll is turning the aircraft such that the sides go up and down (rolling to the left would make an airplane's left wing dip down).
