A smoothing spline is a mathematical tool used in data analysis to create a smooth curve that fits a set of data points. It balances the trade-off between fitting the data closely and maintaining a smooth shape, which helps to avoid overfitting. The method uses piecewise polynomial functions, typically cubic polynomials, to achieve this smoothness. The process involves selecting a parameter, often called the smoothing parameter, which controls the degree of smoothness. A smaller value allows the spline to follow the data more closely, while a larger value results in a smoother curve. This technique is widely used in statistics and machine learning for tasks like trend analysis and interpolation.