Jur é means "I swore" or "I promised." It's the past tense of the verb jurar (to swear/to promise).
In this song, the word jur é is central to the entire narrative. The singer repeatedly emphasizes that he "swore" he would never return, even though he still feels pain and longing. This word captures the song's theme of pride, broken promises, and the struggle between love and self-respect, making it very impactful.
Vicente Fernández's "Juro Que Nunca Volveré" is a powerful declaration of a broken heart's resolve. Our singer has been hurt, and he's not shy about admitting it! He tells his former love, "Podría volver / Pero no vuelvo por orgullo simplemente" [I could come back / But I'm not coming back simply out of pride]. He's made a promise to himself, and he's sticking to it: "Si te juré nunca volver debes creerme / Que cumpliré y mi promesa es no volver" [If I swore to you I'd never come back, you must believe me / That I will fulfill it and my promise is not to return].
He's pretty blunt, actually, telling his ex that "En este mundo nadie es indispensable / Tú puedes ser feliz sin mí y yo sin ti" [In this world, no one is indispensable / You can be happy without me and I without you]. Even though she might be saying she can't live without him, he remembers the pain she caused. He says, "Sufrí bastante que juré nunca volver" [I suffered so much that I swore never to return]. So, when she asks him to come back now, his answer is firm: "Jure que nunca volveré y no volveré" [I swore I'd never return, and I won't return]. It's a song about pride, pain, and sticking to your word, even when it's hard.