Serenatas is the Spanish word for "serenades". It describes the classic romantic gesture of performing a song for a loved one, traditionally sung at night beneath their window.
In this song, Jerry Rivera sings that the person who gives serenatas is now considered old-fashioned. He uses this beautiful, culturally-rich word to evoke a nostalgic and passionate kind of love that he feels is disappearing from the world.
Puerto Rican salsa star Jerry Rivera sounds genuinely annoyed by the modern dating scene in "Amores Como El Nuestro", and his complaints are hilarious because of how dramatic they get. He claims that grand romance is going extinct "como los unicornios" (like unicorns). Shooting stars fall without hearing anyone make a wish, lovers no longer draw hearts on walls, and giving serenades or plucking petals from a rose ("deshojar una rosa") has become a thing for fools ("cosa ya de tontos"). Instead of true devotion, he grumbles that people treat love like a casual fling where "solo es cosa de un beso" (it is just a matter of a kiss), and points out that modern songs only talk about "sábanas mojadas" (wet bedsheets).
Against all that superficial romance, he puts his own relationship on the highest pedestal possible. He compares his bond to Romeo y Julieta (Romeo and Juliet), declaring that real devotion means "darse por completo" (to give oneself completely) and surrender everything the soul feels. Because their devotion is so pure, he insists "no debe morir jamás" (it must never die). It is totally over-the-top, old-school salsa romanticism, but Jerry sells it with absolute conviction.