Desvelo comes from the verb desvelarse, meaning to stay awake or to suffer from sleeplessness. It's a more evocative word than simply saying "no duermo" (I don't sleep).
In "Gris," the artist sings, "Hoy me mata tu recuerdo y me desvelo, deseando un beso." This line beautifully conveys the pain of a lost love, where the memory is so strong it causes him to lie awake at night, longing for a kiss. It captures a deep emotional state of yearning and sleepless nights.
"Gris" is a heartbreak ballad about the ache of missing someone who is gone. The singer hasn't seen or felt them in so long, and every small memory of their presence - the scent of their body, their kisses - is now just an absence.
He keeps looking for them without success, and their phone doesn't get answered anymore. He wonders out loud whether they simply don't want him back at all.
The title says it best: without that person, everything looks gray. The color has gone out of his world, and all that's left is the sad, colorless reality of missing them.