The Nyquist Stability Criterion is a graphical method used in control theory to determine the stability of a feedback system. It involves plotting the frequency response of the open-loop transfer function on the complex plane. By analyzing how the plot encircles the critical point (-1, 0), engineers can assess whether the closed-loop system will remain stable under various conditions. This criterion is particularly useful for systems with time delays and can be applied to both linear and nonlinear systems. It helps in designing controllers by providing insights into how changes in system parameters affect stability, ensuring reliable performance in applications like automotive control and aerospace engineering.