detail from Two sphinxes stand - 'Greek, Attic, red-figure, ca. 520 B.C.' (How to Read Greek Vases, p 109)
The Sphinx was 'a monster with the head of a woman, the body of a lion and the wings of a bird' (Penguin Book of Classical Myths).
In Greek myth the Sphinx is terrible and deadly. The most well-known story about the Sphinx is her harassment of the people of Thebes. She sat by the city gate and would let no one pass. To get into the city, the people had to solve the Sphinx's riddle. If they were not able to solve the riddle, she ate them. Eventually, Oedipus arrives, solves the riddle and the Sphinx is vanquished.
Although the sphinx can be found in myth from other cultures, usually the sphinx is a man-bird and rather benign. Hmm.
For those who are interested in sphinx pottery (and who wouldn't be) or a general introduction to greek vases, I recommend How to Read Greek Vases by Joan R. Mertens (published in 2010 by The Metropolitan Museum of Art, New York in association with Yale University Press, ISBN 9780300155235). The book is easy to follow for the art history novice but covers the main styles/schools of pottery and talks about methods of production.