In the assembly, when the congregation was being directed in prayer, the women were charged to cover their heads as a recognition of submission for the man is head over the woman. Likewise, the men were commanded to pray without their heads covered remembering that they too are in submission to Christ who is the head over the Church.
I gotta disagree here, the subject is HAIR, not some type of covering or cover (oorah)...
1Co 11:4 Every man praying or prophesying, having his head covered, dishonoureth his head.
1Co 11:5 But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven.
1Co 11:6 For if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered.
1Co 11:7 For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.
1Co 11:8 For the man is not of the woman; but the woman of the man.
1Co 11:9 Neither was the man created for the woman; but the woman for the man.
1Co 11:10 For this cause ought the woman to have power on her head because of the angels.
1Co 11:11 Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord.
1Co 11:12 For as the woman is of the man, even so is the man also by the woman; but all things of God.
1Co 11:13 Judge in yourselves: is it comely that a woman pray unto God uncovered?
1Co 11:14
Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?
1Co 11:15
But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.
1Co 11:16
But if any man seem to be contentious, we have no such custom, neither the churches of God.