I take it you mean the head coverings for women spoken of by Paul in 1 Corinthians chapter 11?
1 Cor 11:3-16 NRSV [with comments added]
v. 3 But I want you to understand that Christ is the head of every man, and the husband is the head of his wife, and God is the head of Christ.
The "head” of the husband is Christ. The head of the wife is the husband. The head of Christ is God. The words "man” and "woman” are just as easily translated "husband” and "wife.” Every man is not the "head” of every woman. Paul is describing the relationship of wife to husband and both of them to Christ. This passage does not deal with single people because they are automatically assumed to be under the authority of their parents (in Paul’s day, the age of the single child would have been irrelevant). The discussion is about roles, responsibilities and the hierarchy of "authority” in Christ.
v.4 Any man who prays or prophesies with something on his head disgraces his head,
Paul says that if a man prays or prophesies with his head covered, he dishonours Christ. His "head” represents Christ, and so, symbolically, should not be "covered.”
v. 5 but any woman who prays or prophesies with her head unveiled disgraces her head—it is one and the same thing as having her head shaved.
His wife, in the context of prayer and prophecy, should have her head covered because her head represents her husband and so should be covered, symbolically at least, during communion with God. This acknowledges that, at such times, her only true head is the Lord Jesus Christ. If she is not willing to cover her head, she needs to remove the covering which represents the authority of her husband by having her hair cut off – shorn or "shaved” as Paul puts it. The word means to be shorn like a sheep. Ordinary "short” feminine styles don’t exempt a sister from wearing a head covering. Indeed, if she were shorn at the meeting, would she then have to wear a covering in presence of her husband until her hair grew back?
v. 6 For if a woman will not veil herself, then she should cut off her hair; but if it is disgraceful for a woman to have her hair cut off or to be shaved, she should wear a veil.
Here Paul says, if a woman will not wear the veil during "prayer” and "prophecy” she should then be willing to have her head shaved. From the context, Paul is talking about the three different classes of "fellowship events.” These are the same as those we read about in Acts 2:42 "And they continued steadfastly in the apostles’ doctrine and fellowship, and in breaking of bread, and in prayers.” "Doctrine” would correspond to "Prophesying” in 1 Cor 11 (means to speak forth God’s word) and is equivalent to our Bible Classes and group studies. They had regular meetings for prayer. And, finally, the rest of the chapter, starting at verse 17, deals with behaviour at the Breaking of Bread [communion] where both "praying” and "prophesying” occur.
v.7 For a man ought not to have his head veiled, since he is the image and reflection of God; but woman is the reflection of man.
The divine hierarchy is: God, Christ, Man, Woman. It is a hierarchy of love and service not of domination. Since our relationship to God is mediated by Christ, and the woman or wife is under the authority of her husband, that authority ought to be covered before God because, in Christ, we are all one.
v. 8 Indeed, man was not made from woman, but woman from man. v. 9 Neither was man created for the sake of woman, but woman for the sake of man.
So, he says, since the woman is in the image of man, and was created for her husband, she needs to have her hair, a symbol of that subordinate role veiled. Man, woman, husband, wife in an environment of worship are equal in Christ; equal in privilege and responsibility before God. (Gal. 3:28).
v. 10 For this reason a woman ought to have a symbol of authority on her head, because of the angels.
In an environment of worship, a sister needs to have her head covered to signify her temporary exemption from the authority of her husband. The idea of having "power on her head”[AV] or "symbol of Authority" [NRSV] comes from the Greek word "exousia.” Kittle and Friedrich define "exousia” as first, the ability to perform an action; it then means "right or permission” (as granted by a higher court). She has been given a "court injunction”, so to speak, by God which suspends, during worship, the authority of her husband. "Because of the angels” I think means that we are "formally” in the presence of angels during times of worship in their role as representatives of God. Because of that, a woman is truly as part of the "bride of Christ” with her husband, only under the authority of Christ who is "our head” – our meaning all of us, bond, free, male, and female. This means that in wearing the veil during times of fellowship with God, the authority of her husband is temporarily suspended and her loyalty is directly to God through Christ. It points forward to that time, in the Kingdom of God, when distinctions based on gender will have passed away completely. Far from being a symbol of deference to men, the veil is a symbol of the equality of men and women before God because, in matters of prayer and fellowship, the natural relationships become secondary – Christ is exalted as the true head of the woman and the husband’s authority is covered. It also means that a wife is still responsible to do the right thing before God even if her husband expects her to act differently. She is still personally responsible before God for her actions.
v. 11 Nevertheless, in the Lord woman is not independent of man or man independent of woman.
Paul is careful to keep things in balance. Husband and wife are indispensable to each other.
v. 12 For just as woman came from man, so man comes through woman; but all things come from God.
We are all under God – even the Lord Jesus Christ – and one day we will all, even the Lord, be totally one with Him and subject to Him.
Christ, man/husband, woman/wife will all one day be one and "equal unto the angels.” God is the head over all. Our one true head. The other "headships” are typical of that relationship.
v. 13 Judge for yourselves: is it proper for a woman to pray to God with her head unveiled?
He sums up and says "Judge for yourselves.” Paul is saying, "After what I have just laid out, can you honestly say that it is right for a woman to be in an environment of prayer or divine teaching with her head uncovered?”
v. 14 Does not nature itself teach you that if a man wears long hair, it is degrading to him,
Even in the natural course of things, it is undignified for a man to have "long hair.”
v. 15 but if a woman has long hair, it is her glory? For her hair is given to her for a covering.
A woman’s long hair is her "glory.” It is given to her for a "covering.” Some would say that if a woman has long hair she doesn’t need to wear a covering because her hair IS her covering. However, Paul says that her hair is her GLORY and, in verse 7, he says that the "woman is the GLORY of the man.” Her hair is given to her as a symbol of her subjection to her husband. So, a woman’s long hair is only a covering in the presence of her husband.
In her relationship to God, that whole structure is "covered up” symbolically so that what is represented is the "right” of a woman in Christ to have her own direct relationship with God, equal to that of any husband/brother in Christ.
So the veil is at once a symbol acknowledging the authority of her husband in all things pertaining to their relationship because it acknowledges that her submission to him is suspended in matters of her worship. It is thus an acknowledgement of the equality of a woman/wife in matters of her personal relationship to God.
This is just the opposite of what the world would have us believe. They teach that the covering is a symbol of the domination of women by men and as such should be done away. As usual, such people get the principle wrong. In fact, the principle of head covering is exactly the opposite of what they say!
v. 16 But if anyone is disposed to be contentious—we have no such custom, nor do the churches of God.
Paul brings down the hammer. Here’s how the New Living Translation puts this passage: "But if anyone wants to argue about this, all I can say is that we have no other custom than this, and all the churches of God feel the same way about it.” End of story. Paul has laid out the scripture and meaning and requirements. He is like the judge passing sentence and banging his gavel. God has spoken. Paul says that if you don’t understand it, then just do it as a matter of obedience. (Note that at least 5 translations and 4 paraphrases support this view of v. 16)
Women in the church should wear a head covering at all functions where there is prayer, reading, exposition and/or the partaking of communion. The covering recognizes a womans submission to her husband because, in worship, her subjection is temporarily suspended. The veil is a symbol of the covering of that husband/wife relationship while she is formally in the presence of God (the angels) and of her permission (exousia) to have an independent relationship with God mediated by Christ and not her husband. In this sense, it is the exact opposite of the feminist argument that the covering is an outdated symbol of male domination. It is, in fact, just the opposite. It is a symbol, in the context of worship, of a woman’s freedom and responsibility mediated only by the Lord Jesus himself. Also, given that a wife is the "glory of the man (i.e. her husband)” that glory should be covered because (1Cor 1:29) no flesh should glory in his presence.”
It is symbolic of the woman’s right to an independent relationship with God, unmediated by her husband. The veil represents the covering of the husband’s authority over her in this context. Her hair is her "glory” and is her covering in the presence of her husband and represents her subjection to her husband. She is "the glory of her husband.” The glory and authority of mankind in general and, in her situation, that of her husband in particular, is to be out of sight in the presence of God.
Christ is the only head of both men and women before God and as such must not be covered. The veil is her "permission slip” (exousia) to set aside, in the context of worship, the authority of her husband. Her responsibilities and privileges before God are personal and not mediated by her husband.
Paul says, by the authority of his inspiration, that even if one does not understand his reasoning, the custom of head coverings is mandated in all churches everywhere.
The veil is a symbol of the covering of the flesh in the presence of God (as represented here by the angels). The woman, who is subject to her husband in the normal course of life, stands beside her husband in the church as will the bride of Christ and her Lord in the Kingdom and beyond, equal to one another and, together in Christ, subject only to God.
I hope you have found this helpful.