I believe this comes from an old fable, I had heard the Swan used to be a metaphore for death. So the story runs pretty straight, a jealous sister pushes a younger sister in a river and will not help her unless she leaves her lover. She drowns and becomes a swan - encompassing death, while her sister takes her lover. She floats down the river until she washes up on shore, and is taken by a harp maker to create a beutiful harp out of her remains. Her soul fills the harp and it plays by itself. The harper is so amazed, he wants to show the king. When he brings it before the court, it plays all by itself, and reveals to the court the treachery of her sister, the princess.
I know most of that probably didn't need to be said - I don't think there is great hidden meaning behind the lyrics, I just love this story and this song so much I had to say something :)