Polynomial interpolation is a mathematical method used to estimate values between known data points. By using a polynomial function, which is a mathematical expression involving variables raised to whole number powers, we can create a curve that passes through a set of given points. This allows us to predict unknown values based on the established relationship of the known points. The most common form of polynomial interpolation is the Lagrange interpolation, which constructs a polynomial that exactly fits a set of data points. Another method is Newton's divided difference, which builds the polynomial incrementally. Both methods are useful in various fields, including computer graphics and numerical analysis.