In this passage, head is used both literally and figuratively. A man who covers his physical head while praying dishonors his spiritual head, Christ. A woman who prays or prophesies without covering her physical head dishonors her spiritual head, her husband.
The spiritual gift of prophesying is the God-given ability to speak a specific message from God, not just to predict the future (see 12:10; 14:1–5; 1 Thessalonians 5:20).
every woman who prays or prophesies: Women were allowed to pray and prophesy publicly in the church (see Acts 21:9).