Desvaneciendo means "fading away" or "vanishing". It's a beautiful and evocative word that paints a picture of something slowly disappearing.
In "Media Luna", the lyrics describe a "beso imposible que se va desvaneciendo en su sonrisa" (an impossible kiss that fades away in her smile). This captures the bittersweet feeling of a fleeting moment or a love that can't quite be grasped, making it a poignant and memorable choice.
Los Amigos Invisibles build this song around one image: a woman as la media luna, a half-moon, always partly hidden. The opening line says she's "Que promete descubrirse noche a noche" [that promises to reveal herself night after night], but the singer never gets the rest of her. He's jealous of daylight itself, singing "Por el sol que la amenaza poco a poco" [because the sun threatens her, little by little], as if the sunrise is a rival stealing her back every morning.
He calls her "Reina de mis sueños rotos" [queen of my broken dreams], then a few lines later "Reina de los inocentes" [queen of the innocent] followed right by "De los comediantes, de los incoherentes" [of the comedians, of the incoherent]. Naming three kinds of person in one breath is exactly how obsession talks, tender and unhinged in the same verse. By the last chorus he's the one left over, "Porque me voy quedando solo con la noche" [because I'm left alone with the night], with only the title's half-moon still going around.