I found this on Grace To You site which is very helpful:
Head Coverings For Women
1 Corinthians 11 February 17, 2016 BQ022713
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Every man who has something on his head while praying or prophesying, disgraces his head. But every woman who has her head uncovered while praying or prophesying, disgraces her head; for she is one and the same with her whose head is shaved. For if a woman does not cover her head, let her also have her hair cut off; but if it is disgraceful for a woman to have her hair cut off or her head shaved, let her cover her head. (11:4–6)
It is best to understand that Paul is here referring to activities of believers in ministry before the Lord and the public, where a clear testimony is essential.
In the most general senses praying is talking to God about people, including ourselves, and prophesying is talking to people about God. One is vertical (man to God) and the other is horizontal (man to man), and they represent the two primary dimensions of believers’ ministry. Admittedly, the detail of this passage related to head coverings is difficult because of the scarcity of historical data. But the content helps to clarify the principle Paul has in mind, whatever the special covering may have been. He wants the church to live according to divine standards.
When Paul said a man disgraces his head if he has something on his head while praying or prophesying, he had to be referring to local Corinthian custom. The phrase has something on his head literally means “having down from head,” and is usually taken to refer to a veil. The context here implies that in Corinth such a head covering would have been completely ridiculous for a man and completely proper for a woman. For Jews, who came to wear head coverings, the practice seems to have come in the fourth century A.D., though some may have tried it in the time of the apostles. But generally it was regarded as a disgrace for a man to worship with his head covered.
It seems, therefore, that Paul is not stating a divine universal requirement but simply acknowledging a local custom. The local Christian custom, however, reflected the divine principle. In Corinthian society a man’s praying or prophesying without a head covering was a sign of his authority over women, who were expected to have their heads covered in these ministries. Consequently, for a man to cover his head would be a disgrace, because it suggested a reversal of the proper relationships. Disgraces her head could refer to her own head literally and to her husband’s metaphorically.
In Paul’s day numerous symbols were used to signify the woman’s subordinate relationship to men, particularly of wives to husbands. Usually the symbol was in the form of a head covering, and in the Greek–Roman world of Corinth the symbol apparently was a veil of some kind. In many Near East countries today a married woman’s veil still signifies that she will not expose herself to other men, that her beauty and charms are reserved entirely for her husband, that she does not care even to be noticed by other men. Similarly, in the culture of first–century Corinth wearing a head covering while ministering or worshiping was a woman’s way of stating her devotion and submission to her husband and of demonstrating her commitment to God.
It seems, however, that some women in the Corinthian church were not covering their heads while praying or prophesying. We know from secular history that various movements of women’s liberation and feminism appeared in the Roman empire during New Testament times. Women would often take off their veils or other head coverings and cut their hair in order to look like men. Much as in our own day, some women were demanding to be treated exactly like men and they attacked marriage and the raising of children as unjust restrictions of their rights. They asserted their independence by leaving their husbands and homes, refusing to care for their children, living with other men, demanding jobs traditionally held by men, wearing men’s clothing and hairdos, and by discarding all signs of femininity. It is likely that some of the believers at Corinth were influenced by those movements and, as a sign of protest and independence, refused to cover their heads at appropriate times.
As with meat that had been offered to idols, there was nothing in the wearing or not wearing of the head covering itself that was right or wrong. It is the rebellion against God–ordained roles that is wrong, and in Corinth that rebellion was demonstrated by women praying and prophesying with their heads uncovered.
Dress is largely cultural and, unless what a person wears is immodest or sexually suggestive, it has no moral or spiritual significance. Throughout biblical times, as in many parts of the world today, both men and women wore some type of robe. But there always were some clear distinctions of dress between men and women, most often indicated by hair length and head coverings.
It is the principle of women’s subordination to men, not the particular mark or symbol of that subordination, that Paul is teaching in this passage. The apostle is not laying down a universal principle that Christian women should always worship with their heads covered.
The mention here of women’s praying or prophesying is sometimes used to prove that Paul acknowledged the right of their teaching, preaching, and leading in church worship. But he makes no mention here of the church at worship or in the time of formal teaching. Perhaps he has in view praying or prophesying in public places, rather than in the worship of the congregation. This would certainly fit with the very clear directives in 1 Corinthians (14:34) and in his first letter to Timothy (2:12). The New Testament has no restrictions on a woman’s witnessing in public to others, even to a man. Nor does it prohibit women from taking nonleadership roles of praying with believers or for unbelievers; and there is no restriction from teaching children and other women (cf. Titus 2:3–4; 1 Tim. 5:16). Women may have the gift of prophecy, as did Philip’s four daughters (Acts 21:9), but they are normally not to prophesy in the meetings of the church where men are present.
In other words, it is only necessary to combine the relevant passages to get the composite truth. Women may pray and prophesy within the boundaries of God’s revelation, and with a proper sense of submission. And it is critical that their deportment in so doing reflects God’s order. Certainly they must not appear rebellious against God’s will.
Paul’s point in verses 4–5 is that, whenever and wherever it is appropriate for men and women to pray or prophesy, they should do so with proper distinction between male and female. Every man should speak to or for the Lord clearly as a man, and every woman should speak to or for the Lord clearly as a woman. God does not want the distinction to be blurred.
For a Corinthian woman to pray or prophesy with her head uncovered disgraced or shamed her and made her the same with her whose head is shaved. If a woman took off her head covering she might as well make the symbol of her role rejection complete by taking off all of her hair, the God–given identifier of her special role as a woman. For if a woman does not cover her head, let her also have her hair cut off. In that day only a prostitute or an extreme feminist would shave her head.
The Talmud indicates that a Jew considered a woman with a shaved head extremely ugly, and Chrysostom records that women guilty of adultery had their hair shaved off and were marked as prostitutes. Aristophanes even taught that the mother of unworthy children should have her hair shorn.
Paul therefore is saying, “If you are not willing to look like a prostitute or a rebellious feminist by cutting off your hair, don’t pray or prophesy with your head uncovered either.”
It is remarkable that any Christian woman would seek such an identification, until we think of how some appear today so worldly as to make the same comparison possible.