Newton's interpolation formula is a method used in numerical analysis to estimate values of a function based on known data points. It constructs a polynomial that passes through these points, allowing for predictions of function values at other locations. The formula uses divided differences, which are calculated from the function values at the given points. The formula can be expressed in a form that combines the known values with the corresponding basis polynomials. This approach is particularly useful when dealing with unevenly spaced data points, making it a versatile tool in fields such as computer science and engineering.