System Reponse and Stability
In essense, the system response is the output of the system due to excitation from the input. In the above illustration, the input signal are step function and impulse function respectively, and the output on the right are the corresponding system responses. Here, think of the system as a "black box" that takes an input signal, processes it, and gives an output signal.
Left: Bounded Input Signal, Center: Stable Output (BIBO), Right: Unstable Output.