Marchitó means "withered" or "faded", a word usually used to describe a dying flower. It's a beautifully sad and poetic term you won't hear every day.
In this song, the singer uses it as a powerful metaphor: "Aquel que pisó la rosa y creyó que se marchitó" (The one who stepped on the rose and thought it withered). He's referring to a past lover who hurt the woman he now loves, comparing her to a delicate rose that was damaged but not destroyed, setting the stage for him to help her bloom again.
This salsa classic by Venezuela's Adolescent's Orquesta tells a story from a very specific point of view. The singer is talking to a girl who has been hurt by a previous lover, and he starts off with a surprisingly blunt line: "No finjas, que ya lo sé todo... No es tu primera vez, ya me di cuenta" (Don't pretend, I know everything... It's not your first time, I already noticed). He tells her not to cry, because he's not like the guy who hurt her and he's here to show her what real love is.
He sees himself as her savior, the one chosen to heal her. He gets pretty dramatic about it, saying "Es que Dios me mandó para ti" (It's that God sent me for you) and promises to adore and protect her for life. He asks her to forget her past and give herself to him completely, telling her to laugh because a new life is beginning for them. It's an incredibly passionate and protective declaration of love, where he insists her past doesn't matter and he's the one who will finally treat her right.