Marchita means 'withered', and it's typically used to describe a plant or flower that has dried up. It's a beautifully poetic word you don't often hear in pop songs.
Luis Fonsi creates a powerful image, singing that he has a flower in his pocket that is "marchita de buscar a una mujer" (withered from searching for a woman). This metaphor represents his long and tiring search for love, making the song's core message of 'not giving up' even more moving and hopeful.
This song is a massive anthem of hope and not giving up, especially when it comes to love. Luis Fonsi starts by describing himself as quiet, like a sleeping child who could wake up at any moment: "Soy como un niño dormido / Que puede despertarse / Con apenas sólo un ruido" (I'm like a sleeping child / who can wake up / with just a noise). He's waiting for the right moment to confess his feelings, even if he thinks the other person will just laugh and call him "un loco atrevido" (a crazy, bold person).
The whole feeling is one of powerful, patient determination. He repeats over and over, "Yo no me doy por vencido" (I don't give up), because he wants "un mundo contigo" (a world with you). He's so committed that he swears "vale la pena esperar / Y esperar y esperar un suspiro / Una señal del destino" (it's worth it to wait / and wait and wait for a sigh / a sign from destiny). It's a beautiful song about holding on to a dream, believing you're just one step away from happiness, and having the strength to wait for it.