Marchito comes from the verb marchitar, meaning "to wither" or "to fade." It's a beautiful and evocative word often used to describe plants, but here it's applied to something much more abstract.
In the song, the lyrics speak of "Cada dulce momento que marchito la ciudad" (Every sweet moment that the city withered). It personifies the city as something that can cause precious moments to fade away, highlighting a longing for a simpler, more natural existence away from urban life. This metaphorical use makes it particularly striking.
Monsieur Perine build "Vamonos" around one repeated dream: walking slowly, hand in hand, with time itself stopped. "Sueño con vos con tus ojos negros" ("I dream of you with your black eyes") turns into a comparison that only makes sense sung out loud, "Con tus pupilas brillando como el firmamento" ("With your pupils shining like the firmament"). Barefoot on the grass, inventing words just to see a smile, rain painted as a watercolor of the sky when April comes. None of it is grand. It is just the small stuff someone can't stop replaying.
Then the song admits why it needs the dream. "Hoy el dolor, mi alma solitaria" ("Today the pain, my solitary soul") has pulled away from everything just to find some calm, worn down by a city that took "Cada dulce momento que marchito la ciudad" ("Every sweet moment that the city faded"). The answer is the chorus, said until it stops sounding like a suggestion: "Vámonos, vámonos, vámonos, vámonos lejos" ("Let's go, let's go, let's go, let's go far"). The song cares less about where they end up than about repeating the words enough times to actually leave.