What does 1 Corinthians 11:7 mean?
Paul has endorsed the fact that both men and women pray and prophesy in the Corinthian church services. That action, itself, is not something Paul addresses here. What he has mentioned is appearances—specifically clothing and head coverings—and what those imply to others in that culture. Based on the overwhelming cultural perception of what covered or uncovered heads meant, Paul gives different guidelines for men and women.Corinthian men must not have their heads covered, perhaps by pulling their robes over their heads as the Romans did when worshiping pagan gods. Women, though, must keep their heads covered, as was apparently the custom of the day for all women in public. In that era, a woman with a publicly-uncovered head would be viewed in much the same way as a modern woman wearing a revealing bathing suit in church.
Now Paul begins to explain why this matters. Men are said to be the image and glory of God. Paul appears to be referencing Genesis 1:26: "Then God said, 'Let us make man in our image, after our likeness.'" Man was formed by God from dust in His own image, to become—at that moment—the glory of God's creation. Woman, generally speaking, is the glory of man. Paul will explain in the following verse that this is because Eve was taken out of man, fashioned from Adam's rib, when she was created.
As seen in the context of other Scripture, Paul's intent here is not to disparage the value of women. His meaning must be drawn from the full range of his remarks. The main point of these is what it means when Christians totally ignore the implications of their "freedoms" and dishonor their "head"—spiritually and socially—in the process.