Other people have given you mathematical explanations (it finds values of x such that f(x) = 0). If you want an intuitive geometrical understanding (of the one

Other people have given you mathematical explanations (it finds values of x such that f(x) = 0). If you want an intuitive geometrical understanding (of the one dimensional version, i.e. x and f(x) represent numbers not vectors) try playing with this demo I made: https://www.desmos.com/calculator/kogwanro0d https://www.desmos.com/calculator/kogwanro0d. It shows the way the method follows tangent lines to get each iteration. You can move the orange start point, adjust the function with the b and c sliders, or change the f(x) function formula to another function entirely.