In the same way, an airplane is stable when the combined center of lift of the wing and the tail acts behind the center of gravity. Controllability means that different trim conditions can be commanded. A system might have a natural trim condition, and be stable about the condition, but be uncontrollable, because the operator is unable to command a different condition. A controllable system has actuators to introduce moments that can drive the system to a new position. Imagine that there is a mechanism that can move the support under the seesaw.
Most airplanes have horizontal and vertical tails to make the airplane stable.
These control structures behave like the feathers of an arrow. These surfaces can also be used to control the orientation of the airplane. The horizontal tail has an elevator that controls pitch moments. The vertical tail has a rudder that controls the yaw moments. The airplane also has controls near the tips of the wings called ailerons.