1 Corinthians 11:3-16 addresses the issue of women and head coverings. The context of the entire passage of 1 Corinthians 11:3-16 is submission to the God-given order and "chain of command." A "covering" on a woman's head is used as an illustration of the order, headship, and the authority of God. The key verse of this passage is 1 Corinthians 11:3 "But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God." The implications of this verse are found in the rest of the passage. The order is: God the Father, God the Son, the man or husband, and the woman or wife. The veil or covering on the head of a believing Corinthian wife showed that she was under the authority of her husband, and therefore under submission to God.
Within this passage is also verse 10: "For this reason the woman ought to have a symbol of authority on her head, because of the angels." Why is that important to angels? The relationship of God with men is something that angels watch and learn from (1 Peter 1:12). Therefore, a woman's submission to God's delegated authority over her is an example to angels. The holy angels, who are in perfect and total submission to God, expect that we, as followers of Christ, be the same.
This covering not only means a cloth but also can refer to a woman's hair length. How can we say that? We must take this verse in the context or the setting in which it is presented. "Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering" (1 Corinthians 11:14-15). Therefore, in the context of this passage, a woman who is wearing her hair longer marks herself out distinctively as a woman and not a man. The Apostle Paul is saying here that in the Corinthian culture, when a wife's hair was longer than her husband's, it showed her submission to his headship. The roles of the male and female are designed by God to portray a profound spiritual lesson, that is of submission to the will and the order of God.
But why is hair an issue in this passage? The apostle Paul is addressing an issue related to the Corinthian culture that was being allowed to disrupt the church. For a woman to have a shaved head was a disgrace (and, in Jewish thinking, a sign of mourning, Deuteronomy 21:12). Her hair was her “glory” (1 Corinthians 11:15). In the Corinthian culture, women normally wore a head covering as a symbol of their submission to their husbands. Paul affirms the rightness of following that cultural mandate—to dispense with the head coverings on women would send the entirely wrong signal to the culture at large. In fact, Paul says that, if a Christian woman refuses her head covering, she might as well shave her hair off, too (verse 6). A woman who refused to wear a covering in that culture was basically saying, “I refuse to submit to God’s order.” Therefore, the apostle Paul is teaching the Corinthians that hair length or the wearing of a “covering” by the woman was an outward indication of a heart attitude of submission to God and to His established authority.
God's order is that the husband is the head of the wife as God is the head of Christ, but there is no inequality or inferiority implied. God and Christ are equal and united, just as the husband and the wife are one. This is not a passage that teaches the woman is inferior to man or that she should be submissive to every man. It is teaching God's order and spiritual headship in the marriage relationship. In the Corinthian culture, a woman who covered her head during worship or when she was in public displayed her submission to authority.
In today's culture, we no longer view a woman's wearing of a head covering as a sign of submission. In most modern societies, scarves and hats are fashion accessories. A woman has the choice to wear a head covering if she views it as a sign of her submission to the authority of her husband. However, it is a personal choice and not something that should be used to judge spirituality. The real issue here is the heart attitude of obedience to God's authority and submission to His established order “as to the LORD” (Ephesians 5:22). God is far more concerned with an attitude of submission than an outward display of submission via a head covering. First Timothy 2:9-10, "I also want women to dress modestly, with decency and propriety, not with braided hair or gold or pearls or expensive clothes, but with good deeds, appropriate for women who profess to worship God."