The empennage, also known as the tail assembly, is the rear section of the body of the airplane. Its main purpose is to give stability to the aircraft. The fixed parts are the horizontal stabilizer and the vertical stabilizer or fin.
The horizontal stabilizer is the one responsible for keeping the aircraft nose at the right angle (up or down), preventing the it to pitch up or down. At the rear section, we will see a control surface which is called the elevator which is a movable airfoil that controls the pitch (up-and-down) movement of the aircraft nose.
The vertical stabilizer is responsible for keeping the aircraft nose pointed to the direction of travel, preventing it from yawing back and forth. The principle behind its operation is much like the deep keel on a sailboat. In light, single-engine aircraft, it also serves to offset the tendency of the aircraft to roll in the opposite direction in which the propeller is rotating.
The hinged section of the vertical stabilizer is the rudder, which controls the yaw (left-and-right) movement of the aircraft.