Quick Answer: Controllability is an important property of a control system and plays a crucial role in many regulation problems, such as the stabilization of unstable systems using feedback, tracking problems, obtaining optimal control strategies, or, simply prescribing an input that has a desired effect on the state. Controllability and observability are dual notions. Controllability pertains to regulating the state by a choice of a suitable input, while observability pertains to being able to know the state by observing the output. Broadly speaking, the concept of controllability relates to the ability to steer a system around in its configuration space using only certain admissible manipulations. The exact definition varies depending on the framework or the type of models dealt with.