Banach's Theorem, also known as the Banach Fixed-Point Theorem, is a fundamental result in mathematical analysis that guarantees the existence and uniqueness of fixed points for certain types of functions. Specifically, it applies to contractions on complete metric spaces, meaning that if a function brings points closer together, it will have a unique point that remains unchanged when the function is applied. The theorem is widely used in various fields, including functional analysis and differential equations, to prove the existence of solutions to equations. Its significance lies in providing a systematic way to find fixed points, which are crucial in many mathematical and applied contexts.