Which swan are you talking about?
The plot of the story is Princess Odette, the white swan, loves
Prince Siegfried. Von Rothbart, the evil man, changes Odette into a
swan by day but a girl by night, although his reasoning's are never
made clear. His daughter, Odile, becomes the black swan and tricks
Siegfried into confessing his eternal love for her, thinking it was
Odette. Odette finds Siegfried and shows him that she is not Odile
and kills herself because she can not stand being a swan. Because
Siegfried is in love with her, he kills himself too. The ending
scene is them gaily floating toward heaven.
See the American Ballet's performance in related links.