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 that are difficult to analyze mathematically. It provides insights into how changes in system parameters affect stability, making it a valuable tool for designing robust control systems in various applications, including electronics and automation.