Someone you love is leaving, and you are trying very hard to be okay about it. That is the whole mood here. The singer says she is glad to hear his voice, glad he is finally travelling the way he dreamed, but every line keeps sliding back to the same small sentence: "Te vas y te pierdo" (you leave and I lose you).
The best joke in the song is in the title. He promises to come back "cuando los sapos bailen flamenco" (when the toads dance flamenco), which in Spanish works like "when pigs fly": it means never. She plays along, saying she will wait, "aunque no entiendo bien que los sapos puedan dejar de saltar" (although I don't really get how toads could stop hopping). It is sweet and a little sarcastic at the same time.
The goodbye itself is told in small, sad images: being thrown away like a gift that got dirty, or like a glass after "el trago más dulce" (the sweetest sip). Notice "con mis labios en tus dedos" (with my lips on your fingers): she kisses his hand so she doesn't have to say the scary words out loud. Great song for learning the present tense of everyday verbs like ir, perder and esperar.