Finite Difference Methods are numerical techniques used to approximate solutions to differential equations. They work by replacing continuous derivatives with discrete differences, allowing for the analysis of complex problems in fields like physics, engineering, and finance. This approach is particularly useful for solving partial differential equations, which describe various phenomena such as heat conduction and fluid flow. In these methods, a grid is created over the domain of interest, and the values of the function at grid points are calculated iteratively. By using Taylor series expansions, finite difference approximations can be derived, leading to various schemes like forward, backward, and central differences to estimate derivatives.