The Collaborative International Dictionary of English v.0.48:

Peony \Pe"o*ny\ (p[=e]"[-o]*n[y^]), n.; pl. Peonies
   (p[=e]"[-o]*n[i^]z). [OE. pione, pioine, pioni, OF. pione, F.
   pivoine, L. paeonia, Gr. paiwni`a, fr. Pai`wn, Paia`n, the
   god of healing. Cf. P[ae]an.] (Bot.)
   A plant, and its flower, of the ranunculaceous genus
   P[ae]onia. Of the four or five species, one is a shrub; the
   rest are perennial herbs with showy flowers, often double in
   cultivation. [Written also p[ae]ony, and piony.]
   [1913 Webster]

WordNet (r) 3.0 (2006):

peony
    n 1: any of numerous plants widely cultivated for their showy
         single or double red or pink or white flowers [syn:
         peony, paeony]