Pasional translates to "passionate" and is a less common, more intense way to describe strong emotions than the everyday apasionado.
In this song, Ricky Martin's "Corazón no seas pasional" (Heart, don't be passionate) is a plea to his own heart to resist the overwhelming, fiery love he feels for a woman who is causing him pain. It highlights the internal struggle between reason and intense emotion, making it a compelling word choice.
Ricky Martin spends this whole song arguing with his own heart like it's a separate person who won't listen to reason. He opens with the plea that gives the song its title, "Corazón no vuelvas más con ella" ["Heart, don't go back to her anymore"], and from there it plays less like a love song than an intervention he's staging for himself.
The physical detail is what sells it. "Si la abrazo tiemblo como un papel" ["If I hug her, I tremble like a paper"] is such a specific, almost embarrassing image that you believe he's actually lived it. He knows exactly what's wrong with the relationship too: "Ella es fuego lento besándome" ["She's a slow fire, kissing me"], someone who burns him gradually instead of all at once. By the chorus he's begging his heart to just say goodbye, "Corazón dile adiós" ["Heart, say goodbye"], because he can't quite make himself do it.