The Lagrange interpolation formula is a mathematical method used to estimate the value of a function at a given point based on known values at other points. It constructs a polynomial that passes through a set of given data points, allowing for accurate predictions and analysis. This formula is particularly useful in numerical analysis and computer science. In the formula, each data point contributes a term to the polynomial, weighted by a specific factor that ensures the polynomial equals the known values at those points. The result is a single polynomial that can be evaluated at any point within the range of the data, making it a powerful tool for interpolation tasks.