My comments below cover the entire section, verses 2-16. The NET Bible includes a number of translator notes on this passage that are helpful.
In verse 3 Paul describes a hierarchy of authority as follows:
- God (the Father)
- Man - ἀνήρ (Strongs G435) - "man"; male (adult?); husband
- Woman - γυνή (Strongs G1135) - "woman"; female (adult?), regardless of marital status; wife
Although each instance of "man" in this verse includes a definite article, "woman" does not. If you read Constable's notes in the NET Bible, he takes this to mean that there is a direct relationship between these two - a man and his wife. In other words, according to this view Paul does not mean that every man is an authority over every woman.
"Head" is the translation of κεφαλή (Strongs G2776) - "head"; physically, the nerve center; metaphorically, a superior, chief, lord, authority; origin or source. I've intentionally used the word "authority" here, because I think it's clear from other passages (such as Galatians 3:28) that Paul does not teach superiority of one gender over the other. Furthermore, viewing this as specific to a marital relationship dovetails into passages such as Ephesians 5 or 1 Peter 3 that use very similar language.
Moving on to verses 4-5, Paul introduces a play on words, contrasting between men and women regarding a covering or symbol on their physical head, apparently in light of their metaphoric or spiritual "head". He also uses several different words for "covered" and "uncovered". First, a man should not have his head "covered" - ἔχω (Strongs G2192); to hold or wear (something), possess - while praying or prophesying. To do so brings disgrace on his head - possibly referring to Christ, as opposed to his physical head. Likewise, a woman should not have her head "uncovered" - ἀκατακάλυπτος (Strongs G177); not covered, not veiled (Note the etymology here: the root word is 2619 below, preceded by "ἀ" to indicate an inversion of meaning) - while praying or prophesying, or she disgraces her head - possibly referring to her husband, as opposed to her physical head.
In verse 6, he introduces a new word for "cover" - κατακαλύπτω (Strongs G2619); to cover or veil. He also compares between the humiliation of a woman whose head was shaved or who had short hair - possibly a cultural reference, though I could find little information one way or the other - with a woman who did not have her head covered. The crux of his argument seems to be that it would be shameful for a woman to have short hair or a shaved head, but she brings the same shame by not having her head covered. So he establishes two contrasting statements: Head not covered -> cut off hair. If cut-off hair is shameful -> cover head.
Verses 7-9, 11-12 add a new dimension to the discussion. (Skipping 10 for a moment) Here, he says that a man should not have his head covered, because he is "the image and glory of God", while the woman is the "glory of the man". The word translated "glory" here and below in verse 15 is δόξα (Strongs G1391); opinion, judgment or view; splendor, brightness, magnificence, excellence, dignity, majesty. He then refers back to the creation account in which Eve was formed from Adam's rib. This has three implications:
- From the definition of "head" above, man is the "source" of woman
- Woman was created as a suitable helper for the man
- Neither men or women are independent from one another
Backing up to verse 10 now, Paul introduces a "symbol of authority" - ἐξουσία (Strongs G1891); authority, liberty, strength, privilege, government. However, he does not specify exactly what this symbol should be. Perhaps this is another cultural reference. It is also possible that this refers to an external symbol representing her internal attitude of deference to male leadership in the church, particularly to her husband. (This alludes to a much larger topic that Paul will tackle later in the chapter - but note that his assumption here is that women are actively involved in certain "churchy" behaviors, and that's okay.)
An interesting aside also appears in verse 10 - she should have a symbol of authority on her head "because of the angels." This seems to be a reference that is now lost to us, though the NET Bible notes suggest that this might refer to Ephesians 3:10.
In verse 13-15, Paul now discusses the matter of hair as covering. First, he asks a rhetorical question that assumes (based on the sentence structure) an answer of "no" - "is it proper for a woman to pray with an uncovered head?" Next, he contrasts long hair on men vs. women - his argument states that, just as it would be shameful for a man to have long hair, for a woman to have long hair is her "glory". (See definition of G1391 above.) Furthermore, he states that the woman's long hair has been given to her as a "covering" - περιβόλαιον (Strongs G4018); mantle, veil, wrapper. This is the only appearance of this particular word in the passage, so he seems to be saying something slightly different here than in the previous contexts where a woman's head should be "covered".
Paul concludes in verse 16 with an appeal to the existing practice church-wide. In other words, his comments here mirror the orthopraxy of the church in a universal sense.
Now then, how to apply this? (Maybe a little too doctrinal here? :) )
- If we assume from verse 2 that this was purely a Corinthian cultural teaching with no modern applicability, that seems to make it easy enough to ignore. However:
- Where does this then leave us on the application of passages like Ephesians 5?
- Paul seems pretty adamant in verse 16 that their violation of this is deeper than a cultural matter - it points to an issue of orthodox practice across the church. As well, he may also be pointing out the possible spiritual ramifications mentioned above.
- We could assume that the "covering" is equivalent to the woman's hair.
- Some denominations therefore frown upon women cutting their hair or wearing short styles. However, my personal concern with this is that it's a short road to legalism. "All women shall have hair not less than 36 inches in length.", etc... (True story, related by disconnected tangent: one of my high school teachers had a quirky yet well-kept beard. They moved to another state and joined a new church; he was required to shave, under the reasoning that not everyone was capable of growing a nice-looking beard so men in the church just weren't allowed to have beards - you wouldn't want the ones with beards to feel proud, or the men who couldn't grow one to feel inferior.)
- We might also consider this a cultural tradition, since there doesn't seem to be much concern these days with women wearing short hair styles.
- This view is muddled slightly by verses 10 and 15 - while verse 15 seems to suggest that the woman's hair is her covering, verse 10 suggests that whatever is in scope here should be a symbol of some kind.
- Likewise, the text seems to set up the point that, if a woman would not have the symbol of authority, she ought to cut off her hair too. This makes it difficult to work out that the hair is the symbolic covering, since this would be redundant in these verses - "If a woman won't wear long hair, she should cut off her hair." ??
- Perhaps the scope of the passage is intended to mean a literal, external symbol such as a veil, covering or cap.
- This then needs to be discussed further, based on whether or not this literal symbol is still expected today. Some denominations do so, pointing to this passage as a scriptural mandate.
- If we assume that this is still expected today, then we would need to consider the following as well:
- Does this apply to all women, or only those who are married?
- Do other cultural symbols, such as a wedding band, supercede this?
- Does it apply throughout life, only within the church or (even more narrowly) only when actively engaged in a part of the worship service?
- Likewise, if we take the stance that this was a valid, external symbol for the culture but is not a matter of orthodox practice today, why not?
- As above, is a symbol such as a wedding ring seen as a symbolic replacement?
- Is this ignored today because of our own cultural reasons, because it is "difficult", or because of a simple lack of desire to do so?
My understanding of this passage is probably colored by the fact that I grew up Mennonite - one of the denominations in which a physical veil or covering is still widely normative.
There are several Bible.org articles that cover these details as well, and I've linked some of them below. What's interesting as well is that they each reach somewhat different conclusions.