One of the hardest verses in the Bible is 1st Cor 11:10 "That's why a woman must have authority on her head, because of the angels." (Tom Wright's translation)
There are dispute over the meaning of authority and on the nature of the angels. My personal inclination is that the verse is trying to teach that women must have control over her head. She must not bow to any pressure to "liberate" her dressing to demonstrate her new found freedom in Christianity. Not only is the order of the church important, the angels (representing the created world) are watching whenever we worship.