The Extreme Value Theorem states that if a function is continuous on a closed interval, it must attain both a maximum and a minimum value within that interval. This means that there will be at least one point where the function reaches its highest value and at least one point where it reaches its lowest value. For example, if you have a continuous function like f(x) defined on the interval from a to b, the theorem guarantees that there are points c and d in that interval such that f(c) is the maximum and f(d) is the minimum of the function.