The Quran

يا أَيُّهَا النَّبِيُّ قُل لِأَزواجِكَ وَبَناتِكَ وَنِساءِ المُؤمِنينَ يُدنينَ عَلَيهِنَّ مِن جَلابيبِهِنَّ ۚ ذٰلِكَ أَدنىٰ أَن يُعرَفنَ فَلا يُؤذَينَ ۗ وَكانَ اللَّهُ غَفورًا رَحيمًا

Ali Unal

O (most illustrious) Prophet! Tell your wives and your daughters, as well as the women (wives and daughters) of the believers, to draw over themselves some part of their outer garments (when outside their homes and when before men whom they are not forbidden to marry because of blood relation).¹ This is better and more convenient for them to be recognized (and respected for their decency and decorum) and not harrassed.² God is indeed All-Forgiving, All-Compassionate.³

The verse means that women must cover their heads and upper parts of their bodies. The majority of scholars conclude that they must also cover their faces except the eyes. As understood from the Traditions, this was the practice during the Messenger, upon him be peace and blessings, and the Companions (Abū Dāwūd, “Libās,” 32, “Menāsik,” 34; Imam Mālik, “Hajj,” 16).
There are two important instances of wisdom in ordering Muslim women to cover themselves. Muslim women are women who deserve respect and who are to be protected from any offense or harassment. The veil both shows that they are Muslims, decent, and free (not bondsmaids), and demands protection against any harassment. Although no one can claim that a woman who does not wear a veil desires to attract the attention of men to herself, it is an undeniable and frequently witnessed reality that a woman who displays her charms often exposes herself to unwanted attention.
Despite all contrary assertions in the modern world, God, Who relates the injunction of veiling for women to His infinite forgiveness and compassion, explicitly declared that it is from compassion for women.