Steven Anderson puts it like this:
"According to these verses women should have their heads "covered," and men should not. In fact, if a woman's head is not covered, that is just as bad as if she were "shorn" or "shaven." Notice that the Bible says that it is a "shame" for a woman to be shorn or shaven. We all know what "shaven" means, but what does the word "shorn" mean? The Bible uses the word "shorn" one other time in the New Testament:
Acts 18:18 And Paul after this tarried there yet a good while, and then took his leave of the brethren, and sailed thence into Syria, and with him Priscilla and Aquila; having shorn his head in Cenchrea: for he had a vow.
The vow that the Bible is referring to here is a Nazarite vow from the Old Testament. Notice what the Bible commands about the Nazarite vow in Numbers 6:
Num 6:5 All the days of the vow of his separation there shall no razor come upon his head: until the days be fulfilled, in the which he separateth himself unto the LORD, he shall be holy, and shall let the locks of the hair of his head grow.
Num 6:18 And the Nazarite shall shave the head of his separation at the door of the tabernacle of the congregation, and shall take the hair of the head of his separation, and put it in the fire which is under the sacrifice of the peace offerings.
Once again, the Bible is its own dictionary. Being "shorn" is another word for being "shaven." Paul having his head shaved with a razor is referred to as him being "shorn." Therefore God is saying that a woman being "uncovered" is just as shameful as her shaving her head completely bald as Paul did in Acts 18.
So, what is this "covering"?"
1Cor 11:13 Judge in yourselves: is it comely that a woman pray unto God uncovered?
1Cor 11:14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?
1Cor 11:15 But if a woman have long hair, it is a glory to her: for her hair is given her for a covering. According to verses 13-15, a woman is "uncovered" if she does not have "long hair." A woman is therefore commanded to have long hair, and a man is commanded not to have long hair."
Steven L Anderson: Why Women Should Not Wear Head-Coverings