What does the Quran really say about a Muslim woman's hijab?

Samina Ali TED University of Nevada

‘And say to the believing women that they restrain their eyes and guard their private parts, and they display not their beauty and embellishments except that which is apparent thereof, and that they draw their head-covers over their bosoms, and they display not their beauty or their embellishment thereof save to their husbands, or to their fathers, or the fathers of their husbands, or their sons, or the sons of their husbands, or their brothers or the sons of their brothers, or the sons of their sisters, or their women, or what their right hands possess, or such of male attendants who have no wickedness in them, or young children who have not yet attained any concept of the private parts of women. And they walk not in a style that such of their beauty as they conceal is noticed. And turn you to Allah all together, O believers, that you may succeed.’