Why Do Muslim Women Cover Their Face

Women must wear hijaab. Allaah is the One Who has instructed women to cover their adornments. This includes their bosoms, faces, and any other adornments.

This was enjoined on women to protect them from abuse and temptation. Because women are the focal point of desire and the focus for what those who are tempted view.

A woman who is beautiful will attract people to her. This is the reason for many immoral activities such as adultery, and the things that lead thereto. Therefore, hijaab for women is obligatory and was made mandatory in this aayah below:

And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed. [al-Noor 24:31]

The veil (khimaar), is that which falls from the head and covers one's face. The jilbaab or outer garment is what a woman wears to cover herself and keep her body covered.

And Allaah says:

O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful. (Qur'an 33:59)

QURAN ON HIJAB

O children of Adam, We have bestowed upon you clothing to conceal your private parts and as adornment. But the clothing of righteousness - that is best. That is from the signs of Allah that perhaps they will remember. (Quran 7:26)

HADITH ON HIJAB

Narrated `Aisha:

The wives of the Prophet (ﷺ) used to go to Al-Manasi, a vast open place (near Baqi` at Medina) to answer the call of nature at night. `Umar used to say to the Prophet (ﷺ) "Let your wives be veiled," but Allah's Apostle did not do so. One night Sauda bint Zam`a the wife of the Prophet (ﷺ) went out at `Isha' time and she was a tall lady. `Umar addressed her and said, "I have recognized you, O Sauda." He said so, as he desired eagerly that the verses of Al-Hijab (the observing of veils by the Muslim women) may be revealed. So Allah revealed the verses of "Al-Hijab" (A complete body cover excluding the eyes). – 

Sahih al-Bukhari 146