This paper presents a complete answer to the longstanding unanswered question of what value iteration (VI) is for continuous-time, continuous-state-action space nonlinear systems. Based on this proposed VI, we develop a new data-driven adaptive optimal control methodology for unknown nonlinear systems. As compared with the existing literature of adaptive dynamic programming (ADP) for continuous-time systems which often uses policy iteration (PI), an initial admissible control policy is no longer required. By means of the obtained result, a non-model-based adaptive optimal control design is given. The effectiveness of the proposed methodology is also illustrated by an example.