What does Yoneda's Lemma tell us about a representable functor?

Question

Someone told me that a functor being representable is good because we can use Yoneda's Lemma. But I'm not sure how Yoneda's Lemma tells us anything new given that a functor is representable. For example, say I have a representable functor $F$ from a category $C$ to $Sets$ with representation $(A, \phi).$ This tells me that $Nat(h^A, F) \cong F(A).$ I guess this tells me that $\phi \in Nat(h^A, F)$ can be associated with some $u \in F(A)$ but what else?