Beneficio de la duda is a powerful phrase that translates directly to "the benefit of the doubt". It's a plea for someone to believe you have good intentions, even when circumstances look bad.
In this emotional song, the singer asks his partner for exactly that: a second chance. He's asking her to set aside her judgment and listen to his side of the story, hoping to repair their relationship. It's the central theme and title of the song, making it a key phrase to understand.
This song is a direct plea from someone who knows they messed up. The singer is talking to an ex, admitting right away that he probably doesn't deserve a second chance. He even says, "No me merezco el beneficio de la duda" (I don't deserve the benefit of the doubt). He's not trying to pretend he's perfect; he just wants a chance to tell his side of the story, hoping it won't make him look quite so bad.
His main argument is that what they had was too good to throw away over "estupideces" (stupid things). He makes a very practical, almost selfish point that it's in both their interests to move on from the fight. He warns that it will be difficult for them to find what they had in "otros cuerpos, otras bocas" (other bodies, other mouths). He's basically saying, 'Look, we were great together, and starting over with someone new will be a pain for both of us, so let's just fix this.' It's a bold move, ending with the promise that if she just gives him that one chance, "no te vas a arrepentir" (you won't regret it).