An airplane's stability is inherent to its design. Each airplane exhibits negative, neutral, or positive static stability, as well as negative, neutral, or positive dynamic stability. A more stable airplane requires less effort to control.
Static Stability
Static stability refers to an airplanes initial reaction when displaced. For example, if an airplane's controls were quickly pushed forward, while in straight and level flight, and then released, the airplane would respond according to its static stability. If its initial reaction is to return to the straight and level flight, it has positive static stability. If it initially reacts to the displacement by continuing to move away from straight and level flight, it has negative static stability. If it does neither and, instead, initially reacts by remaining exactly as it was displaced, it has neutral static stability.
Dynamic Stability
Dynamic stability describes the airplane's inherent behavior over time. For example, say an airplane in straight and level flight is pitched up to the climb attitude. The power is not increased from the normal cruise power setting. The pilot then takes his or her hands off the yoke and observes the airplane's dynamic stability.
The airplane slows down as a result of it's higher pitch with no power increase. Less air flows over the flight controls, and they become less effective. The pitching forces of the elevator and elevator trim become unable to maintain the pitch up attitude, and the airplane begins to pitch over on its own.
It pitches down, through the horizon, and goes into a descent. Since power is still constant, the airspeed increases. The flight controls become more effective. The airplane now begins to pitch up on its own, through the horizon once again, and goes into a climb.
If the airplane pitches up and down less and less over time, and eventually returns to more or less level flight, it has positive dynamic stability. An airplane with neutral dynamic stability would maintain roughly the same upward and downward displacements over time, and an airplane with negative dynamic stability would get worse and worse over time.
The typical general aviation airplane is designed with positive static and dynamic stability. Neutral stability might be desirable for an airplane intended for aerobatics. Many airplanes designed for military purposes are negatively stable, as a result of the priorities of those designs.