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 values at points where we do not have data. The most common form of polynomial interpolation is the Lagrange interpolation, which constructs a polynomial that exactly fits a set of points. Another method is Newton's divided difference, which builds the polynomial incrementally. Both methods are useful in fields like computer graphics, data fitting, and numerical analysis.