While studying a given problem we are interested on in what is happening to an object one or a group set of objects that we call system. When As time goes on we can observe changes in the system. For example, while pushing a box we observe that its speed increases. The velocity of the box has changed from some initial value at an initial time, vi(ti), to some final value at a final time, vf(tf). If we consider the system changes ibox to be the system, the change in the system is measured by the change in the box's velocity. In other words, the box's velocity at a given time can describe the state of the system. We say that the system has changed from an initial state to a final state.
It is always useful to sketch the initial and final state of the system. The following is what we call an initial-state and final-state diagram. The dotted circle indicate the system under consideration.