Huracán is a goodbye song, and the singer is the one walking out. It opens with a door slammed shut: "Si te vas, no vuelvas más" (if you leave, don't come back). She regrets "vivir buscando amar en un alma desierta" (living while looking for love in a deserted soul), which is a sharp way to describe a partner who gives nothing back.
The chorus is where the title comes in: "Huracán fueron mis besos en tu piel" (my kisses on your skin were a hurricane). Her love was huge and stormy, and he still stopped loving her, so "yo me voy" (I'm leaving). Watch the phrase "ya no", which means "not anymore", as in "tú ya no me quieres" (you don't love me anymore). It is one of the most useful little phrases in Spanish.