Parthenope was one of the Greek Sirens. The other sirens included Ligeia, Aglaopheme, Peisinoe, Thelxiepeia and Leucosia. The sirens lured sailors to there doom using their voices and music. They were given wings by Demeter in order to aid them in searching for Persephone (abducted by Hades), but were cursed by Demeter when they failed. Circe implies they are cannibals.
Parthenope attempted to drown herself after she failed to entice Odysseus (who had himself tied to the mast of his ship so he wouldn't be able to desert his companions). Her body washed ashore near modern Naples, originally called Parthenope in her honor.
When Napoleon I overthrew the Kingdom of Naples, the French-backed Republic of Parthenope was proclaimed, in memory of her and the original name of Naples. The republic only lasted for 7 months in 1799, until the Kingdom of Naples was restored.