The main body of an airplane is called the fuselage. The role of a fuselage is twofold: It is a base for the rest of the parts, and it carries whatever passengers or cargo the plane is transporting. The fuselage also contains the cockpit, from which the plane is controlled, and the landing gear, which is retracted during flight and lowered for landing. Aside from the fuselage, an airplane's external parts fall into three main categories: those parts that generate movement, those that control movement and those that alter movement.
The basic flight of an airplane has two functions: getting off the ground, and remaining airborne. The thrust to get off the ground is created by the jet engines (in modern jets, in whatever propulsion system the craft uses generally) on the underside of each of the wings. It is the wings themselves that create lift once the plane is in the air, and allow the plane to rest and travel upon the air streams and currents. Along with providing the lift, the wings are a base for other parts of the airplane that allow the pilot to manipulate the plane's movements.
The tail of an airplane has several fins at its end. These fins are called the stabilizers. Two horizontal stabilizers sit on either side of the tail, parallel with the plane's wings. They work to steady the "pitch" (up and down movement) of the plane. One vertical stabilizer sits atop the tail of the plane, and steadies the plane's "yaw" (side-to-side movement). The key to this stabilization is the balance--these stabilizers keep the front of the plane from wandering off course.
Once an airplane is in the air and stabilized, a series of flaps on various parts of the plane control how the movement of the plane is altered. Slats, flaps on the front of the plane's wing, alter lift and aid during take-off. Flaps on the top of the wings, called spoilers, change the shape of the wing, aiding in landing and in balance when the plane is on the ground.
Spoilers can also help the plane turn. Flaps close to the fuselage on each of the wings, these specifically called "flaps," bend downward, creating drag to slow the plane. Flaps further out on the wings, referred to as ailerons, move in opposite directions to cause the plane to turn dramatically. On the tail, the vertical stabilizer contains a rudder, which shifts the plane's yaw, and the horizontal stabilizers contain elevators, which shift the plane's pitch.