The Schauder Fixed Point Theorem is a fundamental result in functional analysis that states if a continuous function maps a convex compact set into itself, then there exists at least one point in that set which is a fixed point. A fixed point is where the function's output equals its input. This theorem is particularly useful in various fields such as economics, game theory, and differential equations. It provides a way to prove the existence of solutions to certain problems by ensuring that a point remains unchanged under the function's application.