What is a state space?
A location in space can be represented using three spatial coordinates, x, y, and z. By analogy, a state space represents a set of different properties of something using coordinates for those properties. A location in the state space, the state, is a unique set of those coordinates.
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve over time.