Ahiru (which translates to duck in Japanese) is in all reality, a duck herself; however, in the beginning of the series she was turned into a human girl by Drosselmeyer. He also bestowed upon her a pendent which causes Ahiru to transform into her other-self, Princess Tutu. This was all caused by her desire to see Myuuto, the Prince of the story, smile. It turns out her role as Princess Tutu is to gather Myuuto's missing heart so he can gain back the many feelings of sadness and happiness.
It is apparent from the start that Ahiru, as a human, duck, and princess, is feverishly in love with the Prince. Regardless, if she confesses her feelings to him she will vanish (or so the story goes). As such, she is stuck in this awful predicament, but she always willingly goes to fetch Myuuto's heart to aid her beloved, lifeless Prince.
In the manga:
Ahiru Arima is human girl that was given a pendant to transform into Princess Tutu. As told by Edel, she gather shards for the Prince to help restore his heart.
In the end of the manga, she does not die or turn into a duck. She forms a friendship with Rue, Fakir, and Myuuto - who she still loves.