Newton's divided difference is a method used in numerical analysis to construct polynomial interpolations. It helps estimate the value of a function at a given point using known values at other points. This technique is particularly useful when dealing with unevenly spaced data points. The divided difference is calculated using a recursive formula, which allows for the efficient computation of coefficients in the interpolation polynomial. By applying Newton's interpolation formula, one can create a polynomial that passes through a set of points, making it easier to approximate values and analyze functions.