Page "Observability" Paragraph 1

Formally, a system is said to be observable if, for any possible sequence of state and control vectors, the current state can be determined in finite time using only the outputs ( this definition is slanted towards the state space representation ).

Less formally, this means that from the system's outputs it is possible to determine the behaviour of the entire system.

If a system is not observable, this means the current values of some of its states cannot be determined through output sensors: this implies that their value is unknown to the controller and, consequently, that it will be unable to fulfil the control specifications referred to these outputs.