The Banach Fixed-Point Theorem, also known as the Contraction Mapping Theorem, states that in a complete metric space, any contraction mapping has a unique fixed point. A contraction mapping is a function that brings points closer together, meaning the distance between the images of two points is less than the distance between the points themselves. This theorem is significant in various fields, including mathematics, computer science, and economics, as it provides a method for proving the existence and uniqueness of solutions to certain equations. It is often used in iterative methods to find solutions, ensuring convergence to the fixed point.