Tell the believing men to lower their gaze and guard their chastity. That is purer for them. Indeed, Allah is acquainted with what they do. And tell the believing women to lower their gaze and guard their chastity and not display their beauty except what [must ordinarily] appear thereof; and to wrap part of their head covers over their chests and not display their beauty except to their husbands, their fathers, their husbands’ fathers, their sons, their husbands’ sons, their brothers or their brothers’ sons, or their sisters’ sons. (Quran 24:30-1)
The additional requirement for women to conceal their adornment and natural beauty is due to their greater need for privacy and protection. Except in the company of close relatives, a woman is required to cover her entire body with loose fitting garments with the exception of her face and hands.
The Qur’an states why Allah has prescribed particular dress regulations for women:
O Prophet, tell your wives and daughters and the women of the believers to draw over themselves their outer garments [when in public]. That is more suitable so they will be known (to be pious believing free women) and not be abused… (Quran 33:59)