Why do Muslim women wear the hijab?

قُل لِّلْمُؤْمِنِينَ يَغُضُّوا۟ مِنْ أَبْصَٰرِهِمْ وَيَحْفَظُوا۟ فُرُوجَهُمْ ۚ ذَٰلِكَ أَزْكَىٰ لَهُمْ ۗ إِنَّ ٱللَّهَ خَبِيرٌۢ بِمَا يَصْنَعُونَ ﴿٣٠﴾ وَقُل لِّلْمُؤْمِنَٰتِ يَغْضُضْنَ مِنْ أَبْصَٰرِهِنَّ وَيَحْفَظْنَ فُرُوجَهُنَّ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنْهَا ۖ وَلْيَضْرِبْنَ بِخُمُرِهِنَّ عَلَىٰ جُيُوبِهِنَّ ۖ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا لِبُعُولَتِهِنَّ أَوْ ءَابَآئِهِنَّ أَوْ ءَابَآءِ بُعُولَتِهِنَّ أَوْ أَبْنَآئِهِنَّ أَوْ أَبْنَآءِ بُعُولَتِهِنَّ أَوْ إِخْوَٰنِهِنَّ أَوْ بَنِىٓ إِخْوَٰنِهِنَّ أَوْ بَنِىٓ أَخَوَٰتِهِنَّ أَوْ نِسَآئِهِنَّ أَوْ مَا مَلَكَتْ أَيْمَٰنُهُنَّ أَوِ ٱلتَّٰبِعِينَ غَيْرِ أُو۟لِى ٱلْإِرْبَةِ مِنَ ٱلرِّجَالِ أَوِ ٱلطِّفْلِ ٱلَّذِينَ لَمْ يَظْهَرُوا۟ عَلَىٰ عَوْرَٰتِ ٱلنِّسَآءِ ۖ وَلَا يَضْرِبْنَ بِأَرْجُلِهِنَّ لِيُعْلَمَ مَا يُخْفِينَ مِن زِينَتِهِنَّ ۚ وَتُوبُوٓا۟ إِلَى ٱللَّهِ جَمِيعًا أَيُّهَ ٱلْمُؤْمِنُونَ لَعَلَّكُمْ تُفْلِحُونَ ﴿٣١﴾

Tell the believing men to lower their gaze and be modest. That is purer for them. Lo! Allah is aware of what they do. And tell the believing women to lower their gaze and be modest, and to display of their adornment only that which is apparent, and to draw their veils over their bosoms, and not to reveal their adornment save to their own husbands or fathers or husbands' fathers, or their sons or their husbands' sons, or their brothers or their brothers' sons or sisters' sons, or their women, or their slaves, or male attendants who lack vigour, or children who know naught of women's nakedness. And let them not stamp their feet so as to reveal what they hide of their adornment. And turn unto Allah together, O believers, in order that ye may succeed.

يَٰٓأَيُّهَا ٱلنَّبِىُّ قُل لِّأَزْوَٰجِكَ وَبَنَاتِكَ وَنِسَآءِ ٱلْمُؤْمِنِينَ يُدْنِينَ عَلَيْهِنَّ مِن جَلَٰبِيبِهِنَّ ۚ ذَٰلِكَ أَدْنَىٰٓ أَن يُعْرَفْنَ فَلَا يُؤْذَيْنَ ۗ وَكَانَ ٱللَّهُ غَفُورًۭا رَّحِيمًۭا ﴿٥٩﴾

O Prophet! Tell thy wives and thy daughters and the women of the believers to draw their cloaks close round them (when they go abroad). That will be better, so that they may be recognised and not annoyed. Allah is ever Forgiving, Merciful.

لَآ إِكْرَاهَ فِى ٱلدِّينِ ۖ قَد تَّبَيَّنَ ٱلرُّشْدُ مِنَ ٱلْغَىِّ ۚ فَمَن يَكْفُرْ بِٱلطَّٰغُوتِ وَيُؤْمِنۢ بِٱللَّهِ فَقَدِ ٱسْتَمْسَكَ بِٱلْعُرْوَةِ ٱلْوُثْقَىٰ لَا ٱنفِصَامَ لَهَا ۗ وَٱللَّهُ سَمِيعٌ عَلِيمٌ ﴿٢٥٦﴾

There is no compulsion in religion. The right direction is henceforth distinct from error. And he who rejecteth false deities and believeth in Allah hath grasped a firm handhold which will never break. Allah is Hearer, Knower.