Banach's Fixed-Point 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 any two points is less than the distance between the points themselves. The theorem guarantees that if you repeatedly apply the contraction mapping, you will converge to this fixed point. This principle is widely used in various fields, including mathematics, computer science, and economics, to solve problems involving iterative processes and to ensure the existence of solutions.