The Hijab is an act of Obedience
The hijaab is an act of obedience to Allah and to his Prophet PBUH, Allah (SWT) says in the Qur'an:
'It is not for a believer, man or woman, when Allah and His messenger have decreed a matter that they should have an option in their decision. And whoever disobeys Allah and His Messenger, has indeed strayed in a plain error'. (33:36)
Allah (SWT) also said: 'And tell the believing women to lower their gaze (from looking at forbidden things) and protect their private parts (from illegal sexual acts, etc) and not to show off their adornment except what must (ordinarily) appear thereof, that they should draw their veils over their Juyubihinna.' (24:31).
Juyubihinna: The respected scholars from As-Salaf As-Saleh (righteous predecessors) differed whether the veil cover of the body must include the hands and face or not. Today, respected scholars say that the hands and face must be covered. Other respected scholars say it is preferable for women to cover their whole bodies.
One view held by the scholars is that the Niqaab (covering the face) is wajib (compulsory) and other scholars hold the view it is Mustahab (recommended and the best thing to do but not compulsory). Niqaab (covering the face) is from the Quraan and Hadith and even if you hold the view of it not being wajib it is still THE BEST thing and recommended and anyone who wears it is to be respected. And if anyone discourages the wearing of Niqaab (covering the face) or denies it being in Islam or makes fun of someone who wears it they should fear ALLAH and take their shahadah over.
The Hijaab is IFFAH (Modesty)
Allah (SWT) made the adherence to the hijaab a manifestation for chastity and modesty. Allah says:
“O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies. That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allaah is Ever Oft‑Forgiving, Most Merciful”
(33:59).
In the above Ayaah there is an evidence that the recognition of the apparent beauty of the woman is harmful to her. When the cause of attraction ends, the restriction is removed. This is illustrated in the case of elderly women who may have lost every aspect of attraction. Allah (SWT) made it permissible for them to lay aside their outer garments and expose their faces and hands reminding, however, that is still better for them to keap their modesty.
The Hijaab is Tahara (Purity)
Allah (SWT) had shown us the hikma (wisdom) behind the legislation of the hijaab:
'And when you ask them (the Prophet's wives) for anything you want, ask them from behind a screen, that is purer for your hearts and their hearts.' (33:53).
The hijaab makes for greater purity for the hearts of believing men and women because it screens against the desire of the heart. Without the hijaab, the heart may or may not desire. That is why the heart is more pure when the sight is blocked (by hijaab) and thus the prevention of fitna (evil actions is very much manifested. The hijaab cuts off the ill thoughts and the greed of the sick hearts:
'Be not soft in speech, lest he in whose heart is a disease (of hypocrisy or evil desire for adultery, etc) should be moved with desire, but speak in an honourable manner.' (33:32)
The Hijaab is a Shield
The Prophet PBUH said: "Allah, Most High, is Heaven, is Ha'yeii (Bashful), Sit'teer (Shielder). He loves Haya' (Bashfulness) and Sitr (Shielding; Covering)." The Prophet PBUH also said: "Any woman who takes off her clothes in other than her husband's house (to show off for unlawful purposes), has broken Allah's shield upon her." The Hadeeth demonstrates that depending upon the kind of action committed there will be either reward (if good) or punishment (if bad).
The Hijaab is Taqwah (Righteousness)
Allah (SWT) says in the Qur'an:
'O children of Adam! We have bestowed raiment upon you to cover yourselves (screen your private parts, etc) and as an adornment. But the raiment of righteousness, that is better.' (7:26).
The widespread forms of dresses in the world today are mostly for show off and hardly taken as a cover and shield of the woman's body. To the believing women, however the purpose is to safeguard their bodies and cover their private parts as a manifestation of the order of Allah. It is an act of Taqwah (righteousness).
The Hijaab is Eeman (Belief or Faith)
Allah (SWT) did not address His words about the hijaab except to the believing women, Al-Mo'minat. In many cases in the Qur'an Allah refers to the "the believing women". Aisha (RA), the wife of the Prophet PBUH, addressed some women from the tribe of Banu Tameem who came to visit her and had light clothes on them, they were improperly dressed: "If indeed you are believing women, then truly this is not the dress of the believing women, and if you are not believing women, then enjoy it."
The Hijaab is Haya' (Bashfulness)
There are two authentic Hadeeth which state: "Each religion has a morality and the morality of Islam is haya." AND "Bashfulness is from belief, and belief is in Al-Jannah (paradise)." The hijaab fits the natural bashfulness which is a part of the nature of women.
The Hijaab is Gheerah
The hijab fits the natural feeling of Gheerah, which is intrinsic in the straight man who does not like people to look at his wife or daughters. Gheerah is a driving emotion that drives the straight man to safeguard women who are related to him from strangers. The straight MUSLIM man has Gheerah for ALL MUSLIM women In response to lust and desire, men look (with desire) at other women while they do not mind that other men do the same to their wives or daughters. The mixing of sexes and absence of hijaab destroys the Gheera in men. Islam considers Gheerah an integral part of faith. The dignity of the wife or daughter or any other Muslim woman must be highly respected and defended.
And ALLAH (SWT) knows best.