Desveló comes from the verb desvelar, which has a dual meaning. It can mean "to keep someone awake" or "to reveal/unveil something."
In this song, Dani Martín uses it poetically when he sings, "Robando el sueño, así nos desveló" (Stealing our sleep, thus it kept us awake/revealed us). This line cleverly plays on both meanings, suggesting that the
"Caminar" opens with a search: "Busco el beso, la revolución" ("I search for the kiss, the revolution"). Dani Martín wants a message that "hable más de amor" ("speaks more of love") in a world he pictures as already broken, and he asks for the courage to face down the wolf that lied to everyone and hear it say sorry to the child it fooled.
The chorus strips all of that down to one word: "Caminar" ("Walk"). Just "poner sonrisa a cada paso y respirar" ("put a smile on every step and breathe"), because "será bonito lo que quede por llegar" ("what is yet to come will be beautiful"). He tells himself to look straight ahead and never lower his gaze again, and to "Retirar" ("remove") whatever ugly mask is holding him back. September can try to take his hope away. He keeps walking anyway, and the song never once raises its voice to make that point.