Repent2God, I'm not sure whether you were sure where to find the scripture of what you were asking so I put it in the subject line of my reply. The scripture that you're referring to is I Cor. 11:6 where it says: '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.'
Now, lets disect this scripture so that you can understand what Paul was saying when he was addressing the church at Corinth. In order to understand one line of scripture you first must read what was said prior to. In verse 1-3 Paul tells the church at Corinth to continue to pattern themselves as he is, which is to say, to continue following Christ as he is. He admonishes the church to understand the 'ORDER' of leadership: Christ being the Head of every man, the head of a woman is her husband, and the Head of Christ is God. Now, going back to the scripture that you are dealing with Paul is stating that the woman is covered by her husband, however as verse 7 states: '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'
What this chapter is dealing with is the fact that there must be order in following or patterning ourselves towards following Christ. It is not talking about the length of a woman's hair, or whether a woman is to wear a hat every time she enters a church. What this scripture is talking about is 'Order' plain and simple. The woman's covering is her husband, if she is not married, her covering is her Pastor.