Lyapunov's direct method is a technique used in control theory and dynamical systems to assess the stability of equilibrium points in nonlinear systems. It involves constructing a Lyapunov function, which is a scalar function that helps determine whether the system's state will converge to an equilibrium point over time. If the function decreases along the trajectories of the system, stability can be inferred. The method is particularly useful because it does not require solving the system's differential equations. Instead, it focuses on the properties of the Lyapunov function to provide insights into the system's behavior, making it a powerful tool for engineers and mathematicians.