In Final Fantasy V, she'll appear as both an alive and dead creature, with her appearance changing along with each incarnation. Her alive appearance resembles a beautiful maiden, though after she becomes undead this fact alters completely and she's quite purple.
Siren is better known as a Summon, however, in the same series. Her first appearance as a summon was in Final Fantasy VI. In this game, the most noteworthy information is the fact that in North America they censored her rear, which was visible in the Japanese version. They did the same for the Game Boy Advance remake, though didn't take as much of a dramatic approach to it (see left).
The origin of the Sirens' name obviously comes from Greek mythology. In the mythology, the story of Odysseus is told in the epic poem known as The Odyssey. In it, when traveling back home via a boat, three Sirens appear (depending on which version the reader is reading, as in some there are only two). Their voice is so beautiful that they are capable of luring in anyone and then ultimately killing them. Odysseus told his sailors to plus their ears with beeswax, though he himself wanted to hear the voices. Though to do so without being lured in, he ordered his sailors to tie him up to the ship's mast.