Palpita means 'beats' or 'pulsates', often referring to a heart beating. It's a more evocative and poetic word than the common 'late' (to beat).
In the song, the lyrics say, "No ha visto que eres muy bonita que tu corazón todavía palpita" (He hasn't seen that you are very beautiful, that your heart still beats). This highlights the idea that despite being unappreciated, her heart is still full of life and emotion, making it a powerful and memorable word in this context.
Jhonny Rivera's "Te Amo En Silencio" is a passionate confession of love, but it's a love that has to stay hidden. Our singer is absolutely smitten, telling us, "siento que me estoy muriendo te amo el silencio" [I feel like I'm dying, I love you in silence]. He's so overwhelmed he can barely stand it, "siento que ya no resisto y lo grito al viento" [I feel like I can't resist anymore and I shout it to the wind].
There's a big problem though: the person he loves is already taken. He laments, "siento que he llegado tarde que ya tienes tu niño que soy cuento aparte" [I feel like I arrived late, that you already have your child, that I'm a separate story]. He truly believes he could make her happy, saying, "yo si te haría feliz porque te amo te adoro te pienso" [I would make you happy because I love you, I adore you, I think of you]. He even goes as far as to say her current partner doesn't appreciate her, "él no te merece es tonto o tal vez es ciego no sabes lo que tiene" [he doesn't deserve you, he's foolish or perhaps blind, he doesn't know what he has]. It's a bold move, but he's clearly desperate to express his feelings, even if it has to be in secret.