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 most common types are the forward, backward, and central differences. These methods allow for the estimation of rates of change and are essential in solving differential equations, especially when dealing with complex systems where analytical solutions are difficult to obtain.