In God's infinite wisdom He saw fit to tell us through Paul--who himself had a great knowledge and understanding of the Kingdom of God--that women should have their head covered. This covering is the authority covering them, or as we've seen that some translations include 'the sign/symbol of' authority. I would present the humble opinion that this truth is totally relevant, important and fully connected to the history of man and that its meaning will become more fully understood. Regardless of how much we understand it though, it would be foolish to disregard this admonition.
I believe that symbol is an outward expression of a woman's submission to the protective authority of her husband or father. That this is connected to the angels very likely (I can find no other biblical explanation) could refer to how certain angels had relations with the daughters of men and produced the giant races spoken of in Genesis in defiance of God's law of reproduction. Jude also touches on these 'Angels who kept not to their estate...but went after other flesh' (likely quoting from the book of Enoch, which is not in the Biblical canon, but includes more details about these events than does Genesis).
That God has given women a special covering for their protection is evident in that generally speaking, women are more easily deceived than men. Eve was first deceived and then she led Adam to sin. It was to the daughters of men that the angels (sons of God--always referring to angels in Genesis) came.
We must now ask ourselves, where was Adam in the case of Eve, and the men in the case of the angels? Why wasn't their protective authority put into action? These questions make me wonder then if the covering of hair for the woman serves also as a sign to her man of his role as protector and husband. The sign is most definitely because of the angels, but it's purpose is to bring both man and woman into their rightful, God-given roles. Another way of looking at it is that not only is a woman's uncut hair a sign of her submission to her husband of father, but also it is a protection from demonic influences. I am certain we will understand more on this topic in the future.
God bless you