The Schauder Fixed-Point Theorem is a fundamental result in mathematical analysis, particularly in the field of functional analysis. It states that if a continuous function maps a convex compact subset of a Banach space into itself, then there exists at least one point in that subset which is a fixed point. A fixed point is where the function's output equals its input. This theorem is significant because it provides a way to guarantee solutions to various problems in mathematics and applied fields. It is often used in differential equations, game theory, and economics to demonstrate the existence of equilibrium points or solutions under certain conditions.