First, let's review. A subject is the <em>who </em>or <em>what </em>of a sentence, while the predicate is the what is <em>happening</em> in the sentence.
So the simple subject is a noun, while the simple predicate is the verb. The predicate also describes what the subject is doing.
In the sentence, "The cheetah is the fastest land animal," the subject would be the cheetah and the predicate would be, "fastest... land animal."