Desvelado literally means "without sleep" and describes the state of being up all night. It's a more poetic way to say you're sleepless, often because you're consumed by powerful emotions like love, worry, or inspiration.
In the song, the singer is desvelado because he wanders the streets all night, obsessively searching for a mysterious woman whose voice he heard on the radio. This single word perfectly captures the romantic longing and restlessness at the very heart of the lyrics.
Have you ever fallen in love with someone you've never even met? In "Desvelado," the singer has done exactly that. He's completely obsessed with a "voz de ternura" (voice of tenderness) he heard, probably on the radio. It's a bit of a wild idea, but he's all in, admitting he fell in love even though "nunca la conocí" (I never met her). He spends his days dreaming of her and listening to the radio, hoping to hear her again.
This isn't just a simple crush, though. It's taken over his whole life! He walks the streets all night, totally "desvelado" (sleepless), searching for this mystery woman. The longing is so intense that his desire "no me deja descansar" (won't let me rest), and he even wakes up crying. He ends the song with a promise to keep searching, telling her, "Te lo juro que te voy a encontrar" (I swear I'm going to find you). It's a dramatic story of searching for a fantasy love.