Desvelo comes from the verb desvelarse, which means to stay awake, often due to worry, excitement, or deep thought. It's more profound than simply 'no dormir' (not sleeping).
In the song, Morad sings, "Sabes que por ti me desvelo" (You know I stay awake for you). This line beautifully conveys a sense of longing, preoccupation, or even suffering caused by thoughts of the other person, making it a very evocative and relatable word in a romantic context.
This song is all about the confusion and frustration after a breakup. Morad and Rvfv are trying to figure out an ex-girlfriend who keeps sending mixed signals. They wonder if she's just trying to make them jealous, asking, "¿Será que lo hace para ver si yo me altero? ¿Será que lo hace para ver si me desespero?" [Could it be she does it to see if I get upset? Could it be she does it to see if I get desperate?]. They even speculate that maybe her new relationship isn't working out, asking, "¿Será su nuevo novio que no la quiere?" [Could it be her new boyfriend doesn't love her?].
Throughout the song, the singers swing between acting tough and admitting they're still hurt. Morad claims he's moved on, saying his heart is full because "mi madre ha llenado todo ese aforo" [my mother has filled all that space], but then Rvfv admits, "siento como algo dentro se muere" [I feel like something inside me dies] if he doesn't see her. They're convinced she's not over them either, with the brilliant line, "Ella tiene un nuevo novio, pero a ese novio le pone mi cara" [She has a new boyfriend, but she puts my face on that boyfriend]. It's a classic case of two people who are no longer together but are still completely tangled up in each other's lives.