The Lyapunov Exponent is a measure used in mathematics and dynamical systems to quantify the rate of separation of two nearby trajectories. It indicates how sensitive a system is to initial conditions; a positive exponent suggests that small differences in starting points can lead to vastly different outcomes, a hallmark of chaotic behavior. In practical terms, the Lyapunov Exponent helps in understanding stability in systems, such as weather patterns or financial markets. By analyzing the exponent, researchers can predict whether a system will remain stable or become unpredictable over time, aiding in various fields like physics, engineering, and economics.