Despierto literally translates to "awake". It's a common word, but its usage in this song is what makes it special and poetic.
In the lyrics, J Balvin sings, "Pero te soñé despierto" (But I dreamed of you while awake). This beautiful contradiction is a Spanish way of saying you're daydreaming or thinking about someone so intensely that it feels like a vivid dream. It perfectly captures the song's theme of being haunted by the memory of a past love.
Have you ever felt completely over your ex until the DJ plays that one specific track? That is the entire vibe of LA CANCIÓN by Colombian star J Balvin and Puerto Rico's Bad Bunny. The narrator heads out for a night of drinking, feeling completely detached with an empty heart, boasting that he even learned English power ballads to move past the breakup: "Hasta me aprendí todas las baladas en inglés" (I even learned all the ballads in English). Bad Bunny brings in sharp pop-culture references too, joking that she was his "fantasía oscura de Kanye West" (Kanye West's dark fantasy, nodding to the famous album) and admitting that casual flings did nothing to erase her memory.
Then the mood shifts entirely when the beat drops and they hear the melody: "Pensaba que te había olvidado / Pero pusieron la canción" (I thought I had forgotten you / But they played the song). Suddenly, every messy, passionate memory comes rushing back, from kissing while totally drunk ("bien borrachos") to sneaking around her parents' house ("casa de tu pa'i", short for papá). J Balvin is happy she is doing well with someone new, but hearing that old favorite tune makes him laugh at himself because, deep down, he never actually moved on.