‘A’isha reported that;
the wives of Allah’s Messenger (may peace be upon him) used to go out in the cover of night when they went to open fields (in the outskirts of Medina) for easing themselves. ‘Umar binKhattab used to say: Allah’s Messenger, ask your ladies to observe veil, but Allah’s Messenger (may peace be upon him) did not do that. So there went out Sauda, daughter of Zarn’a, the wife of Allah’s Messenger (may peace be upon him), during one of the nights when it was dark. She was a tall statured lady. ‘Umar called her saying: Sauda, we recognise you. (He did this with
the hope that the verses pertaining to veil would be revealed.) ‘A’isha said: Allah, the Exalted and Glorious, then revealed the verses pertaining to veil.
(Muslim, Book 26 : Hadith 5397 )

 

Here Allah(swt) said in the nearest meaning: ( 31 ) 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.

The evidence from this verse that hijab is obligatory for women is as follows: 

(a) Allaah commands the believing women to guard their chastity, and the command to guard their chastity also a command to follow all the means of doing that. No rational person would doubt that one of the means of doing so is covering the face, because uncovering it causes people to look at it and enjoy its beauty, and thence to initiate contact. The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The eyes commit zina and their zina is by looking…” then he said, “… and the private part confirms that or denies it.” Narrated by al-Bukhaari, 6612; Muslim, 2657.

If covering the face is one of the means of guarding one’s chastity, then it is enjoined, because the means come under the same ruling as the ends.

(b) Allaah says (interpretation of the meaning): “…and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms)  …”. The jayb (pl. juyoob) is the neck opening of a garment and the khimaar (veil) is that with which a woman covers her head. If a woman is commanded to draw her veil over the neck opening of her garment then she is commanded to cover her face, either because that is implied or by analogy. If it is obligatory to cover the throat and chest, then it is more appropriate to cover the face because it is the site of beauty and attraction.

(c) Allaah has forbidden showing all adornment except that which is apparent, which is that which one cannot help showing, such as the outside of one’s garment. Hence Allaah says (interpretation of the meaning): “…except only that which is apparent …” and He did not say, except that which they show of it. Some of the salaf, such as Ibn Mas’ood, al-Hasan, Ibn Sireen and others interpreted the phrase “except only that which is apparent” as meaning the outer garment and clothes, and what shows from beneath the outer garment (i.e., the hem of one’s dress etc.). Then He again forbids showing one’s adornment except to those for whom He makes an exception. This indicates that the second adornment mentioned is something other than the first adornment. The first adornment is the external adornment which appears to everyone and cannot be hidden. The second adornment is the inward adornment (including the face). If it were permissible for this adornment to be seen by everyone, there would be no point to the general wording in the first instance and this exception made in the second.

(d) Allaah grants a concession allowing a woman to show her inward adornments to “old male servants who lack vigour”, i.e. servants who are men who have no desire, and to small children who have not reached the age of desire and have not seen the ‘awrahs of women. This indicates two things:

1 – That showing inward adornments to non-mahrams is not permissible except to these two types of people.

2 – That the reason for this ruling is the fear that men may be tempted by the woman and fall in love with her. Undoubtedly the face is the site of beauty and attraction, so concealing it is obligatory lest men who do feel desire be attracted and tempted by her.

(e) The words (interpretation of the meaning): “And let them not stamp their feet so as to reveal what they hide of their adornment” mean that a woman should not stamp her feet so as to make known hidden adornments such as anklets and the like. If a woman is forbidden to stamp her feet lest men be tempted by what they hear of the sound of her anklets etc., then what about uncovering the face?

Which is the greater source of temptation – a man hearing the anklets of a woman whom he does not know who she is or whether she is beautiful, or whether she is young or old, or ugly or pretty? Or his looking at a beautiful youthful face that attracts him and invites him to look at it?

Every man who has any desire for women will know which of the two temptations is greater and which deserves to be hidden and concealed.

(ii)

Allaah says (interpretation of the meaning):

“And as for women past childbearing who do not expect wedlock, it is no sin on them if they discard their (outer) clothing in such a way as not to show their adornment. But to refrain (i.e. not to discard their outer clothing) is better for them. And Allaah is All‑Hearer, All‑Knower”

[al-Noor 24:60]

The evidence from this verse is that Allaah states that there is no sin on old women who have no hope of marriage because men have no desire for them, due to their old age (if they discard their outer clothing), subject to the condition that their intention in doing so is not to make a wanton display of themselves. The fact that this ruling applies only to old women indicates that the ruling is different for young women who still hope to get married. If the ruling on discarding the outer clothing applied to all, there would be no point in singling out old women here.

The phrase “in such a way as not to show their adornment” offers further proof that hijab is obligatory for young women who hope to marry, because usually when they uncover their faces the intention is to make a wanton display (tabarruj) and to show off their beauty and make men look at them and admire them etc. Those who do otherwise are rare, and the ruling does not apply to rare cases.

(Reference:Islamic Q & A)