Palpitar means "to beat" specifically in reference to a heart or pulse. While "latir" is a more common verb for a heart beating, "palpitar" carries a slightly more poetic and intense connotation, suggesting a strong, vibrant throb.
In the song, Adriana Lucia sings, "por saber lo que siente al palpitar tu corazón" (to know what your heart feels when it beats). This word choice beautifully emphasizes the deep emotional connection and the desire to understand the innermost feelings of another person.
The song opens by counting. "Cuántas veces yo te volveré a querer?" (How many times will I love you again?) is followed by "Cuántas veces sin saber me equivoqué" (How many times did I go wrong without knowing it?), and the tally she is really keeping is of the times fear won: "Tuve miedo y por temor no me arriesgué" (I was afraid, and out of fear I didn't take the risk). This time she decides to go with her instinct instead.
What she offers after that is deliberately small and physical rather than grand. "Puedo ser como un rayito de sol" (I can be like a little ray of sunshine), "Como lluvia en el verano, florecita de algodón" (Like rain in the summer, a little cotton flower), "La luz en la madrugada, formar parte de tu piel" (The light at dawn, to be part of your skin). The line she keeps returning to is the plainest one, "y que no olvides jamás" (and that you never forget) — running straight into the title phrase, "Que puedo ser" (That I can be), which she then repeats and leaves hanging, with nothing after "be", so the offer stays open rather than closing on a promise.