In ancient Greek mythology, the Empusa (Εμπουσα — Empousa) was a female supernatural monster or demoness. Hecate sent Empusa to harass travelers. It scared to death or ate anybody that travelled along the paths or roads it inhabited.
Empusa is the daughter of the goddess Hecate. The Lamiae and Mormolyceia, who assumed the form of handsome women for the purpose of attracting young men, and then sucked their blood like vampyrs and ate their flesh, were reckoned among the Empusae. (Philostr Vit. Apoll. iv. 25; Suid. s. v.)
The empusae are sometimes described as having donkey-like features and/or bronze feet. It was believed usually to appear with one leg of brass and the other of an ass. (Aristoph Ran. 294, Eccles. 1094.) Whenever a traveller addressed the monster with insulting words, it used to flee and utter a shrill sound. (Philostr Vit. Apoll. ii. 4.) This demonic female has and the occupation of pursuing travelers and eating them - although one can save oneself by insulting her.
Empusa also has the remarkable ability of transforming herself. Sometimes she transforms herself into a gorgeous woman to seduce young men, she then sucks blood from them until they die. By the slightest insult, she flees.
Empusa is best known for her appearance in Aristophanes's The Frogs, in which she scared Dionysus and Xanthias on their way to the underworld.
Suidas s.v. Empuosa (trans. Suda On Line) (Byzantine Greek Lexicon C10th A.D.) :
Empousa. A phantasma daimonios (demonic ghost) sent by Hekate and appearing to the ill-fated. [Something] which seems to change into many forms. Aristophanes in Frogs [indicates this]. [It is called] Empousa from the fact that it moves on one leg (heni podizein), i.e. that its other leg is bronze. Or because it used to appear from dark places to the initiated. She was also called Oinopole. But others say [that it bore this name] because it changed form. It also seems to appear in the light of day, when they are offering sacrifices to the dead. Some say that she is the same as Hekate. But [another name for her is] Onokole, because she has an ass's leg; which they call manure (bolitinon), that is donkey manure. For bolitos [is] the proper word for donkey excrement. Aristophanes in Frogs [says] : `by Zeus, I see a huge wild beast.--What kind?--Terrible. It appears to be everywhere at once: at times it is a cow, then a mule, then again a most beautiful woman.--Where is she? I’m heading towards her.--She is no longer a woman, but a dog now.--It is Empousa, then.--At any rate the whole face is glowing with fire and she has a bronze leg.
Bell, Women of Classical Mythology (sourced from Aristophanes Frogs 294; Aristophanes Ecclesiazusae 1094; Philostratus Life of Apollonius of Tyana 2.4 & 4.25; Suidas s.v. Empusa) :
EMPUSA was yet another female monster. She was in the train of Hecate and originally was sent out to frighten travellers. She was supposed to have on leg of brass and one of an ass. This absurd combination lends a certain comical effect rather than one of horror. Moreover, a traveller could rout the monster with insulting words, causing her to flee with a shrill shrieking. Naughty children were threatened with visits from this awkward creature. But the Empusae (plural for Empusa) were not comical at all when it came to their real design--luring men, especially young ones, to bed. For this purpose they could turn themselves into beautiful women, in which shape they sucked the blood from their victims and ate their flesh. In this respect they were related to the Lamiae and Mormolyceia.