Cholesky Decomposition is a mathematical technique used to simplify the process of solving systems of linear equations, particularly when dealing with symmetric and positive-definite matrices. It breaks down a matrix into the product of a lower triangular matrix and its transpose, making calculations more efficient. This method is particularly useful in various fields such as statistics, machine learning, and engineering, where it helps in optimizing algorithms and improving numerical stability. By transforming complex matrix operations into simpler ones, Cholesky Decomposition enhances computational performance in applications like Gaussian processes and Kalman filters.