Marchitar means "to wither" or "to fade." It's a beautiful and evocative verb often used to describe flowers losing their freshness, but it can also be applied metaphorically.
In this song, Christian Nodal uses it to express his fear that his love, like roses, might eventually wither and fade away. He sings, "Es que me di cuenta que después de días se empezaban a marchitar" (I realized that after a few days they started to wither), referring to roses, but implying a deeper concern about the longevity of his relationship. This word adds a poetic and slightly melancholic touch to the lyrics.
Christian Nodal's "Que Te Olvide" [That I Forget You] is a passionate plea from someone who's tired of their partner threatening to leave. He starts by explaining that he stopped giving roses, not because he doesn't care, but because "después de días se empezaban a marchitar" [after a few days they would start to wilt]. He didn't want her to think their love would fade like that, insisting "Nuestro amor es diferente" [Our love is different].
But now she's full of doubts and says she's going to leave, speaking words he knows she doesn't mean. He begs her, "No vuelvas a pedirme que te olvide" [Don't ask me to forget you again]. He tells her not to silence her heart when her body says otherwise, because "Lo que ocultan tus labios Me lo grita tu piel" [What your lips hide, your skin screams to me]. He warns her not to try and fool herself, because what she feels is unforgettable, and she might not realize "Que me puedes perder" [That you can lose me]. He ends with a powerful warning: "Cuidado con lo que me estás pidiendo Que si te olvido lo hago para siempre" [Be careful what you're asking me, because if I forget you, I'll do it forever].