Letargo translates to "lethargy" or "slumber." It's a less common word in everyday Spanish, making it stand out in the lyrics.
In the song, Laura Pausini sings, "Eres el sueño de mi soledad, un letargo de azul." Here, "letargo de azul" poetically describes a deep, dreamlike state of blue, evoking a sense of calm and profound emotion rather than just simple tiredness. It adds a beautiful, almost mystical layer to the romantic imagery.
The whole song is a list of things the singer is handing over, and the first one sets the tone: "Te regalo una rosa" (I give you a rose). It is not a rose bought for the occasion, either. She found it lying in the road and has no idea what state it is in: "No sé si está desnuda" (I don't know if it's naked), "O tiene un solo vestido" (Or has just one dress). By the second verse the gifts have stopped being objects at all. She offers her hands, her "párpados caídos" (drooping eyelids), "El beso más profundo" (The deepest kiss), and then "Un día entre abril y junio" (A day between April and June), which is not a day anyone can actually give away.
The chorus is where Juan Luis Guerra's writing goes properly strange, and Pausini sings it completely straight. "Yo soy satélite y tú eres mi sol" (I am a satellite and you are my sun) is ordinary enough. Then comes "Un universo de agua mineral" (A universe of mineral water), and "Un letargo de azul" (A lethargy of blue). Mineral water is such a flat, supermarket sort of thing to set beside a universe that it should not work at all, and it does. This is the Italian singer's Spanish covers album, so she is taking on a bachata that Dominican audiences have known by heart for decades, and the smartest thing she does is leave those images exactly where Guerra put them.