Fundamentally Why We Cover

"And say to the believing women that they should lower their gaze and guard their modesty; that they should not display theri beauty and ornaments except what (must ordinarily) appear thereof, that they should draw theri veils over their bosoms adn not display their beauty except to their husbands, tathers, husbands' fathers, sons, or their sisters' sons, or their women or the slaves whom their right hand possess or male servants free of physical needs, or small children who have no sence of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! Turn ye all together towards Allah(S.W.T) that ye may attain Bliss." (Al Qur'an 24:31)