Mischievous nymphs were said to hide in the petals of the Peony thus casing this magnificent flower to be given the meaning of Shame or Bashfulness in the Language of Flowers. It was named after Pæon, a physician to the gods, who obtained the plant on Mount Olympus from the mother of Apollo. Once planted the Peony likes to be left alone and punishes those who try to move it by not flowering again for several years. Once established, however, it produces splendid blooms each year or decades. (Taken from The Language of Flowers, edited by Sheila Pickles, 1990)
Peonies are also extensively grown as ornamental plants for their very large, often scented flowers.
http://en.wikipedia.org/wiki/Peony