Cuento literally translates to "story" or "tale," often one you'd tell a child. In this song of heartbreak, however, the word is used with a much sharper and more dismissive meaning.
When the singer says, "Pero ese cuento ya se acabó" (But that story is over now), he's rejecting his ex-partner's narrative. He's calling their excuses a mere cuento—a fantasy or a lie that he is no longer willing to believe. It's a powerful way to declare that the charade is finally over.
This song is the ultimate breakup anthem for when you're feeling hurt but also a little bit confident. The singer is fed up with being in a one-sided relationship, telling his ex how sad it is "amar a otra persona / Que no te sepa valorar" (to love someone who doesn't know how to value you). He feels like his time has been completely wasted and he can't get it back.
But this isn't just a sad song. He's also telling her that she's making a huge mistake. He challenges her to "Búscate a otro que te pueda dar / Lo mismo que yo" (Find someone else who can give you what I did), knowing she won't. The whole mood flips to this bold claim that he's irreplaceable, summed up in the title line: "Soy el único" (I'm the only one). It's that perfect mix of heartbreak and self-assurance.