Rolle's Theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), where f(a) = f(b), then there exists at least one number c in the open interval (a,b) where the derivative f'(c) is equal to 0. The document provides an example of applying Rolle's Theorem to the polynomial function f(x) = x^2 - 2.5x + 1.5 on the interval [1,2], showing that the derivative is 0 at x = 1.5.