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Stability is a property of many systems. It means being at rest, not liable to change. In mechanics and dynamics, a system is stable (has stability) if it will not change motion of its own accord, and will resist small efforts to change its direction or position.
Thus an airliner in flight is dynamically stable, and will keep going in the same direction even when buffeted by uneven air pressure (wind). To change its direction, its control system must be altered. On the other hand, a fighter plane is unstable, and must be controlled at all times by a combination of the pilot and a computer.
Most nuclear isotopes are unstable, but the world is mostly made of stable ones.