The Arabic text of this ayah is:
Wa qul li al-mu'minat yaghdudna min absarihinna wa yahfazna furujahunna wa laa yubdina zenatahunna illa maa zahara min haa wal-yadribna bi khumurihinna ala juyubihinna; wa laa yubdina zenatahunna illa li bu'ulatihinna aw aba'ihinna aw aba'i bu'ulatihinna aw abna'ihinna aw abna'i bu'ulatihinna aw ikhwanihinna aw bani ikhwanihinna aw bani akhawatihinna aw nisa'ihinna aw maa malakat aymanu hunna aw at-tabi'ina ghayri ulu'l-irbat min ar-rijal aw at-tifl alladhina lam yazharu ala awrat an-nisa wa laa yadribna bi arjulihinna li yu'lama maa yukhfina min zenatahinna. Wa tubu ilaAllahi jami'an, ayyuha al-mu'minun la'allakum tuflihun
A translation of this is:
And say to the faithful women to lower their gazes, and to guard their private parts, and not to display their adornment except what is apparent of it, and to extend their headcoverings (khimars) to cover their bosoms (jaybs), and not to display their adornment except to their husbands, or their fathers, or their husband's fathers, or their sons, or their husband's sons, or their brothers, or their brothers' sons, or their sisters' sons, or their womenfolk, or what their right hands rule (slaves), or the followers from the men who do not feel sexual desire, or the small children to whom the nakedness of women is not apparent, and not to strike their feet (on the ground) so as to make known what they hide of their adornments. And turn in repentance to God together, O you the faithful, in order that you are successful
As we can see, this ayah contains six commands for the Muslim sister, which I will list briefly, inshallah.
1) Lower the gaze.
2) Guard the private parts.
3) Not display the adornment "except what is apparent of it".
4) Draw the khimar to cover the jayb.
5) Not display the adornment except to the people listed in the ayah.
6) Not stamp the feet so as to give knowledge of hidden adornment.
Three of these commands relate to behavior, which are lowering the gaze, guarding the private parts, and not stamping the feet. The other three relate to dress. It can also be noted that commands 3 and 5 are actually parts of the same command. Thus there are two basic rules for the dress of the Muslim sister:
A) Not display the adornment except "what is apparent of it" except to the people listed in the ayah.
B) Draw the khimar to cover the jayb.
There are three things that need to be explained in this:
1) What does "what is apparent of it" refer to?
2) What type of garment is the khimar?
3) What is the woman's jayb?
Inshallah, I will deal with each of these questions in turn.
What does "what is apparent of it" refer to?
There is a difference of opinion on this, and was even among the Sahaba (rAa). The opinion of Abdullah ibn Masud (rAa) is that "what is apparent of it" refers to the outer surface of the woman's garments. This would not permit any of her body to be seen whatsoever (uncovering one or both eyes is a concession to necessity).
The other opinion is that "what is apparent of it" refers to the face and hands and/or to the decorations that are worn on the face and the hands. This is the opinion of Aisha Umm al-Muminin (rAa), Anas ibn Malik (rAa), Abdullah ibn Abbas (rAa), and Miswar ibn Makhrama (rAa) - these are all Sahaba - and also of Ata (rAa), Qatada (rAa), Sa'id ibn Jubayr (rAa), Mujahid (rAa), al-Dahhak (rAa), and al-Hasan (rAa) - these are all Tabi'un (rAa). Almost every tafsir (commentary on the Quran) will include some if not all of these authorities for this opinion.
Among the commentators themselves, some of the most respected have followed the "face and hands" opinion. Among these are Imam Tabari, Imam Zamakhshari, Imam Fakhr ad-Din Razi, and Imam Qurtubi. Here is what they have written in their own words.
Imam Abu Jafar Tabari
"The strongest and most accurate view is that which says that the exemption refers to the face and the hands. Also included are kohl, rings, bracelets, and makeup. We say that this is the strongest and most accurate opinion because all scholars are unanimous that everyone who needs to pray must cover the awra in his or her salat. A woman may reveal the face and the hands in her salat, while she must cover the rest of her body. What is not awra is not haram to be revealed" from his tafsir of Surah an-Nur ayah 31, this is in Volume 18, pages 118-119 of Jami Bayan Ta'wil al-Qur'an
Imam Abu'l-Qasim Zamakhshari
"Why is the woman permitted to display 'what is apparent of it'? Because to conceal that would cause her inconvenience. A woman is forced to deal in commodities with her hands. She is compelled by genuine need to expose her face especially at the times of giving evidence, litigating in court, and marriage. She is compelled to walk the streets and expose her feet, especially poor women. This is the meaning of 'illa maa zahara min ha', that is, what the situations of ordinary life compel her to expose" from his tafsir of Surah an-Nur ayah 31
Imam Fakhr ad-Din Razi
"Since the showing of the face and hands is necessary, the jurists had no choice but to agree that they are not awra" from his tafsir of Surah an-Nur ayah 31
Imam Abu Abdullah Qurtubi
"Since the normal case is that a woman’s face and hands are revealed by the force of habit and for worship, as this is required in salat and hajj, then it is appropriate to say that the exemption applies to these" from his tafsir of Surah an-Nur ayah 31
From this, we can see that the predominant opinion on the meaning of "what is apparent of it" is that it refers to the face and hands. In the context of the ayah, it means that around non-mahram men, women are allowed to display their faces and their hands. This is the exemption that God has given. Everything else must be covered.
What type of garment is the khimar?
In common usage, the words "head" and "face" are distinct. Unless specified otherwise, the word "head" is not taken to refer to the face, but instead refers to the rest of the head, while the word "face" is specially used to designate the face. An example of this is the process of wudu; the Quran and hadiths mention washing the "face" separately from wiping the "head", and we do not again run our hands over the face when we get to the stage of wiping the head. In order to say that the khimar is a garment which covers the face, therefore, it must be specified that it covers the "face". If the khimar just covers the "head" then the general meaning is that it covers the hair. If you think about how we use these words, inshallah you will see that I am correct.
Keeping this in mind, here are some definitions of the khimar and what it means in classical Arabic:
Imam Abu'l-Fida ibn Kathir:
"Khumur is the plural of khimar which means something that covers, and is what is used to cover the head. This is what is known among the people as a khimar."
The dictionary of classical Arabic, Aqrab al-Mawarid:
"[The word khimar refers to] all such pieces of cloth which are used to cover the head. It is a piece of cloth which is used by a woman to cover her head."
Shaykh Muhammad al-Munajjid on Islam Q&A:
"Khimaar comes from the word khamr, the root meaning of which is to cover. For example, the Prophet (peace and blessings of Allaah be upon him) said: “Khammiru aaniyatakum (cover your vessels).” Everything that covers something else is called its khimaar. But in common usage khimaar has come to be used as a name for the garment with which a woman covers her head; in some cases this does not go against the linguistic meaning of khimaar. Some of the fuqahaa’ have defined it as that which covers the head, the temples and the neck. The difference between the hijaab and the khimaar is that the hijaab is something which covers all of a woman’s body, whilst the khimaar in general is something with which a woman covers her head."
Shaykh Muhammad Nasiruddin Albani:
"The word khimaar linguistically means only a head covering. Whenever it is mentioned in general terms, this is what is intended."
Now, in case my argument presented above about "covering the head" versus "covering the face" does not seem convincing, we can also look at what some tafsirs say about the exact meaning of the commandment in Surah an-Nur ayah 31 regarding the khimar:
Imam Abu Abdullah Qurtubi:
"Women in those days used to cover their heads with the khimar, throwing its ends upon their backs. This left the neck and the upper part of the chest bare, along with the ears, in the manner of the Christians. Then God commanded them to cover those parts with the khimar."
Imam Abu'l-Fida ibn Kathir:
"'Draw their khumur to cover their bosoms' means that they should wear the khimar in such a way that they cover their chests so that they will be different from the women of the jahiliyyah who did not do that but would pass in front of men with their chests uncovered and with their necks, forelocks, hair and earrings uncovered."
Both Imam Qurtubi and Imam ibn Kathir are agreed that the women of jahiliyyah (in imitation of the Christian women, according to Imam Qurtubi) used to wear the khimar to cover their hair, but they threw its ends upon their backs. This sloppy way of wearing the khimar exposed the forehead, ears, neck, and upper chest. Subsequently, God ordered them to draw their khimars to cover themselves. It is easy to see how pulling the ends forward again and pulling the khimar tightly around the circle of the face then fastening it at the throat, letting the ends fall downwards, would cover the forehead, ears, neck, and upper chest, as Imam Qurtubi and Imam ibn Kathir have specified. It should also be easy to recognize in this a description of the headscarf of the Muslim sister.
The point is, neither Imam Qurtubi nor Imam ibn Kathir describes that the khimar was to be pulled over the face, even though each specifies a variety of anatomical features of the woman.
This should be strong evidence that the word khimar means HEADSCARF. Its linguistic meaning is a headcovering, not a face veil, and the information provided by both Imam Qurtubi and Imam ibn Kathir clearly shows that the khimar is to be worn as a HEADSCARF not as a face veil.
What is the woman's jayb?
Actually, the quotes from Imam Qurtubi and Imam ibn Kathir provide a pretty good explanation of what the jayb is. The usual translation of the term is "bosom". The word "jayb" has also given its name to a certain type of mathematical curve (see The Origin of the Word Sine).
As well, Surah al-Qasas ayah 32 in Arabic reads "Usluk yadaka fii JAYB ka takhrur bayda'a..." which means "Thrust your hand into your chest and it will come out white..." (this is a story about the prophet Musa, alayhi salam).
Shaykh Muhammad Nasiruddin Albani says that the word "jayb" is related to the word "jawb" which refers to something cut out, and he says that in this context it refers to the neckline of the woman's dress.
In any case, all of these definitions clearly point to the bosom, the upper chest, or the neck and upper chest. They certainly do not mean "face" or "entire body"!
Surah an-Nur ayah 31 gives two basic commands in regard to women's dress. The first of these commands is that the Muslim sister shall cover all of her beauty except "what is apparent of it" whenever non-mahram men are present. The majority opinion on the meaning of "what is apparent of it" is the face and hands.
The second command is to draw the khimar to cover the jayb. In classical Arabic, the khimar is the headcovering or headscarf, and the jayb is the bosom or more generally the neck and upper chest. Imam Qurtubi and Imam ibn Kathir have provided a precise description of how the khimar is to be drawn to cover the jayb, and why this was necessary. Neither the word "khimar" nor the word "jayb" has anything to do with the face.
Therefore, the first command (to cover the beauty) contains a specific exemption that the majority of scholars have taken to refer to the face and the hands. And the second command (regarding the wearing of the khimar) does not mandate the covering of the face either.
In conclusion, I feel that there is a very strong case to be made that Surah an-Nur ayah 31 does not make niqab fard, but in fact allows the display of the face and hands.