Saddle points refer to critical points in a mathematical function where the gradient is zero, but the point is neither a local minimum nor maximum. Instead, it is a point where the function changes from increasing to decreasing, or vice versa. Saddle points play an important role in optimization problems, as they can influence the convergence of optimization algorithms. Additionally, saddle points are commonly found in high-dimensional spaces and can pose challenges for gradient-based optimization methods. Researchers often study saddle points to better understand their impact on optimization and develop more effective algorithms for dealing with them.