What does stability mean in control systems?

A system is stable if its output remains bounded for any bounded input (BIBO stability). For linear systems, this means all poles must have negative real parts (lie in left half of s-plane). An unstable system's output grows unbounded, potentially causing damage. Marginally stable systems (poles on imaginary axis) produce sustained oscillations. Stability is the first requirement in control system design - an unstable closed-loop system is dangerous and useless.