Newton's method is an iterative numerical technique used to find approximate solutions to equations, particularly for finding roots. It starts with an initial guess and improves that guess by using the function and its derivative. The formula involves taking the current guess, subtracting the function value divided by the derivative value, and repeating this process until the guess converges to a solution. This method is particularly effective for functions that are continuous and differentiable near the root. However, it may not always converge, especially if the initial guess is far from the actual root or if the function has certain characteristics, such as flat regions or multiple roots.