The Sphinx lived on the mountain Φίκιο and was a monster who spread panic all over the area. She had the head and the breasts of a woman, legs and tail of a lion (in other versions: of a dragon) and wings of a eagle. Her parents were Τυφωέα and Έχιδνα. She was sent by Hera or Apollo to Thebes to punish the city for the crime of Laius.
Other versions say that Sphinx was actually the female leader of thieves that lived near Thebes. These rogues would assault and kill the citizens who crossed them, leaving no survivors to pinpoint them or even describe them to others. The riddles of the Sphinx were actually traps that the thieves would set up… But this is a boring version so I’ll stick to the Sphinx being a horrid monster who ate and killed whoever answered her wrong.
Source: Ρίσπεν Ζ., Ελληνική Μυθολογία, Εκδόσεις Τριήρης, Τόμος 5ος, σ.742