Secarse is a reflexive verb that literally translates to 'to dry up' or 'to wither', much like a plant deprived of water.
In this passionate song, Enrique Iglesias sings, "Puede secarse mi alma" (My soul could dry up). He uses this dramatic metaphor to declare that even if his very spirit withers away, his memories of this love will remain forever.
Enrique Iglesias is not messing around in this song. He makes one of the biggest promises you can possibly make: no matter what happens, he will never forget the person he's singing to. And he means no matter what. He lays out some pretty extreme scenarios, saying even if "Pueden pasar tres mil años" (Three thousand years can pass) or "Pueden borrar mi memoria" (They can erase my memory), his memory of this person will survive. It's a huge, dramatic declaration of love that lasts forever.
He then asks a series of questions that show us exactly what he can't forget. It's not just a vague feeling; he remembers specific things like their smile and their "locuras" (craziness). He even admits he prayed for them not to leave. The song ends with the ultimate statement of how much this person means to him: he still loves them "Más que a vivir, más que a nada" (More than living, more than anything). It's a classic, over-the-top pop ballad about a love that simply cannot be erased.