Convencerme means "convince me." It's an engaging word because it immediately suggests a plea or a struggle within the song's narrative. It's not an everyday word in the same way as common verbs, making it stand out.
In the context of the song, the singer repeatedly asks, "¿Qué tengo que hacer para convencerme?" (What do I have to do to convince myself/you?). This highlights the emotional turmoil and desperation of the singer trying to either convince himself that his love is true or convince his beloved to return, adding a layer of dramatic tension to the lyrics.
This song is a passionate plea from someone who is completely lost without their love. The singer feels like their life is slowly slipping away, "poquito a poco se me va la vida" [little by little my life is slipping away], ever since their partner left. They're searching for them, but it's clear they're gone: "buscando portaban y te fuiste semana" [searching for you and you left last week].
It's all about the pain of a love lost and the desperate desire for their return. The singer declares, "yo perdí todo por quererte" [I lost everything for loving you], and wonders what they need to do to convince their love to come back. They're ready to give their "vida entera" [entire life] to be with this person forever. It's a really heartfelt and intense expression of longing!