Escribiéndola means "writing it." It's a gerund form of "escribir" (to write) combined with the direct object pronoun "la" (it), referring to their story.
In the song, the artists sing, "Aún no termina nuestra historia, a ver sigamos escribiéndola" (Our story isn't over yet, let's keep writing it). This word beautifully captures the idea of actively continuing and shaping their relationship, making it a compelling and hopeful image for learners.
Cali Y El Dandee wrote this as a straight-up apology song. It opens on two nights of silence: "Otra noche extrañándote" (Another night missing you) and "Otro día más sin hablarte" (Another day without talking to you). He's been sitting with what he did, and it's eating at him. The image that carries the whole song comes early: "Mi corazón en la mitad" (my heart in half), "Y tú la otra parte" (And you the other part). He's not whole without her, plain and simple, and he owns his part in the breakup too: "Dejé en la casa a mi ego" (I left my ego at home), no excuses, just showing up. The chorus repeats the ask like he means it: "Déjame volverte a querer" (let me love you again), "Déjame volver abrazarte" (let me hug you again).
The closing lines are the best part. Instead of promising flowers or grand gestures, he bets on time itself: "Porque sé que va a amanecer" (because I know it's going to dawn), "Y el sol que se fue va a volver" (And the sun that left will return). It's a simple bet, and a little stubborn. The night always ends.