While nota can literally mean a musical 'note' or a written 'note', in this song it's used as popular slang for a 'vibe' or a 'high'. It describes a specific state of mind, often an intoxicating feeling.
In 'Nota de Amor', the artists aren't singing about a written message. They sing "No hay quien me quite esta nota, que estoy sintiendo por ti" (No one can take this high/feeling from me, that I'm feeling for you), describing the powerful and addictive 'high' of being in love. Understanding this one word is the key to unlocking the whole meaning of the song!
This song is one giant, over-the-top love letter! The title, "Nota De Amor," translates to "Love Note," but in this context, nota is slang for a feeling or a high. So, the singers are basically saying they're high on love. They feel so euphoric that they are "Vivo en la luna por ti, vuelo sin alas por ti" (I live on the moon for you, I fly without wings for you). It's a feeling so strong that nothing can bring them down.
Each artist tries to one-up the others with their declarations. Wisin is ready to propose, saying, "en el bolsillo ya tengo el anillo" (I already have the ring in my pocket). Daddy Yankee says this woman makes him forget all others and that dancing a vallenato with her is worth more than all his money. It's all about finding that one person who is your "otra mitad" (other half) and makes you feel completely addicted to their love.