Pontryagin's Maximum Principle is a fundamental concept in optimal control theory, which helps determine the best possible control strategy for a dynamic system. It provides necessary conditions for optimality, allowing one to find the control that maximizes or minimizes a given performance criterion over time. The principle involves formulating a Hamiltonian function that combines the system's dynamics and the performance index. By analyzing this function, one can derive conditions that the optimal control must satisfy, leading to a solution that guides decision-making in various fields, including economics, engineering, and robotics.