I've been known to be grumpy about supposed applications of the Yoneda lemma but here's a cute one.
Picture this situation: you arrived at the post office, and there some people already there waiting for their turn. They are not in a line though, or tickets to get to be called by the tellers. Yet, it does not matter: somehow the correct order emerges from the fact each person knows exactly the set of people which come before them in said order.
This truism is in fact precisely the Yoneda Lemma for posets. You have a set \(P\) (the people waiting in the post office) and each \(p \in P\) has a set \(B_p \subseteq P\) of people that, definitionally, come before \(p\) in the order. We also know that \(p \leq q\) if and only if \(B_p \subseteq B_q\) (\(p\) comes before \(q\) if every person in front of \(p\) is also in front of \(q\), and vice versa). The Yoneda lemma tells me that this is enough to recover \((P, \leq )\): just let \(p \leq q := p \in B_q\).