A spline interpolates data—that is, fills the gaps between known points. Between two adjacent points a spline is an ordinary polynomial. The simplest spline is a connecting line (a linear spline), but here we consider quadratics.
The energy-balance model is fundamental in climate science. In broad strokes, it shows the sensitivity of global temperature to energy from the sun, how much energy is reflected, and how much is absorbed in the atmosphere. The sliders below control these three effects, and the plot shows the resulting stead-state temperature. See this blab for the simulation details.