Juro is the first-person conjugation of the verb jurar, meaning "to swear" or "to take an oath". It's a word packed with emotion and sincerity, used to make a very serious promise.
In this classic ballad, Cristian Castro sings, "Yo te juro que no trataré de olvidarte" (I swear to you that I won't try to forget you). Using juro turns his farewell promise into a powerful, unbreakable vow, showcasing the depth of his feelings even as he's leaving.
Mexican pop singer Cristian Castro brings pure, dramatic devotion to "Nunca Voy A Olvidarte" (I Will Never Forget You). Instead of getting angry about a breakup, the singer accepts his partner's choice to end things with "Ahora voy a marcharme / Pues tú lo decidiste" (Now I am going to leave / Because you decided so). He packs up the good memories like keepsakes—"Junté lo más hermoso / Que viví yo contigo" (I gathered the most beautiful things / That I lived with you)—and leaves with warm wishes, thanking his ex for the happy times with "Tú me hiciste feliz" (You made me happy).
Then comes the delightfully stubborn twist in the chorus. He agrees to leave, but he refuses to move on. He makes a solemn promise: "Yo te juro que no trataré de olvidarte" (I swear to you that I will not try to forget you). He uses the dramatic Spanish idiom "Yo te quiero a morir" (literally 'I love you to death', meaning he loves her beyond measure or to the extreme), showing that no matter where his ex goes, his feelings will stay completely frozen in time.