Finite differences are a mathematical technique used to approximate derivatives and analyze functions. They involve calculating the differences between function values at specific points, which helps in understanding how a function changes. This method is particularly useful in numerical analysis and can be applied to various fields, including physics and engineering. In finite difference methods, the simplest form is the first-order difference, which measures the change between two consecutive points. More complex forms, like second-order differences, can provide better approximations. These techniques are essential in solving differential equations and are widely used in computational algorithms, such as those found in numerical simulations.