APA Dictionary of Psychology

a smoothed mathematical representation of a disjointed or disaggregated relationship between an independent variable (x) and a dependent variable (y), in which values of y vary sharply for different intervals of x. Each range of x thus has a different slope, and spline functions are formed by joining piecewise polynomials at fixed points called knots. Spline functions (or splines for short) are useful for fitting data that have random components, and are widely used for interpolation and approximation of data sampled at a discrete set of points (e.g., for time-series interpolation).