The Hessian is a mathematical concept used in optimization and calculus. It is a square matrix of second-order partial derivatives of a scalar-valued function. The Hessian provides information about the local curvature of the function, helping to determine whether a point is a local minimum, local maximum, or a saddle point. In machine learning and statistics, the Hessian is often used in algorithms for training models, such as Newton's method. By analyzing the Hessian, practitioners can make more informed decisions about how to adjust parameters to minimize error or improve performance.