Cuerno literally means "horn," like on an animal. However, it's also a key part of a hugely popular Spanish idiom: "poner los cuernos," which means "to cheat on someone."
In this song, Bad Bunny makes a clever play on words. He sings that his ex wanted a fantasy love with "unicornios" (unicorns), but instead, "sólo te dieron el cuerno" (they only gave you the horn), a witty line implying she was cheated on. This powerful twist is what makes the word so memorable in the song.
In "BYE ME FUI", Puerto Rican hitmaker Bad Bunny draws a hard line against being treated like a backup plan. He sings to an ex who only comes running back when someone else lets her down ("Viniste buscándome / Porque te fallaron de nuevo" ["You came looking for me / Because they failed you again"]). Instead of playing along, he declares that the game is over and tells her to say goodbye to her best option ("Dile adiós a tu mejor opción / Bye, me fui" ["Say goodbye to your best option / Bye, I left"]). He vents about being tired of being "un por si acaso" ["a 'just in case'"], pointing out how her own mother was crazy about having him as a son-in-law ("Tu mai' loca de que yo sea su yerno" ["Your mom crazy for me to be her son-in-law"]).
Bad Bunny delivers some hilariously blunt wordplay to roast the situation. He mocks her search for a fairy-tale romance: "Y tú que siempre querías / Un amor de fantasía, como los unicornios / Pero sólo te dieron el cuerno" ["And you who always wanted / A fantasy love, like unicorns / But they only gave you the horn"]. In Spanish, "poner el cuerno" is a common idiom that means cheating on someone, so he cleverly flips her unicorn fantasy into a joke about infidelity. He also jokes about bad astrology, wondering if "piscis no mezcla con capricornio" ["Pisces doesn't mix with Capricorn"]. Even though he admits he still craves her, he refuses hot-and-cold games ("Un día sí, un día no, eso no es tenernos" ["One day yes, one day no, that's not having each other"]) and packs his bags for good.