Renglones literally translates to "lines of text" or "rows". It's a more formal and less common word than simply saying "palabras" (words) or "letras" (letters).
In the song, the narrator asks, "¿Qué decían esos renglones de ti?" (What did those lines say about you?). This refers to the content of a letter that revealed his partner's infidelity, making the word intriguing as it hints at a hidden message within written lines.
This song, "En el Olvido" by Binomio de Oro de América, is a classic tale of heartbreak and betrayal, but with a surprisingly strong message of moving on. Our singer finds out his love is cheating when he intercepts a letter meant for her. He doesn't even need to read it to know what's up, saying, "No la quise leer / Porque ahí comprendí que tu me eras infiel" [I didn't want to read it / Because then I understood that you were unfaithful to me]. Ouch!
He was totally dreaming of a future with her, even "Dibujaba tu figura entre el mar y la arena" [I drew your figure between the sea and the sand], imagining marriage. But now, all those dreams are shattered. The pain he thought was gone has returned, and he admits, "Lo que pasó con mi vida / No se lo he deseado a nadie" [What happened with my life / I haven't wished it on anyone]. But here's the cool part: instead of wishing her ill, he actually wishes her well! He hopes she's happy with the other guy, even if he's a bit sarcastic about it. He even warns her not to do the same thing to her new love, because he's found a way to overcome the resentment: "Ahora puedo vencer / El rencor / Con mi nuevo querer" [Now I can conquer / The resentment / With my new love]. That's a powerful message of healing!