"The veil was a sign of guilt and shame worn by the Jew in worship to signify condemnation before the law. But what has the Christian to do with such a sign when professing that, 'Christ hath redeemed us from the curse of the law,' and 'There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit,' (Romans 8:1). For such believers to wear a sign of condemnation is to nullify the worth of the atonement, and so dishonor Christ who released them from the condemnation of the law."--Katharine Bushnell
Before we can delve into the actual text of 1 Corinthians 11: 3-16, we must set the stage to get a feel for the context and unique situation Paul was dealing with when he composed his instructions to the Corinthian Church.
Corinth was a Greek City situated on the peninsula of Southern Greece and was part of the Roman Empire during the time Corinthians was written. Before 146 B.C., Corinth was known for its military might, commercial capabilities, and for its excessive worship of the love goddess, Aphrodite. The city erected a temple dedicated to her, staffed with up to a thousand temple-slaves and courtesans. Prostitution became so ubiquitous in Corinth that the phrase "to corinthianize" became slang for "practicing fornication." This went on until the Romans destroyed the city in 146 B.C. and its citizens were dragged off into slavery. In 44 B.C., the city was refounded by Julius Caesar and became a Roman colony. It regained prominence by 27 B.C., becoming the capital of of the Roman province, Achaia. This resurrection set the stage for Corinth to become a cultural melting-pot, where Roman, Greek, and Jewish cultures found themselves coexisting, conflicting, overlapping and sometimes, colliding.
Corinth became the wealthiest city in Greece during the first century A.D., with a possible population of 600,000. The city returned to its roots and reestablished the temple of Aphrodite during this time. The gods of Apollo, Asclepius, Poseidon, Hermes, Artermis, Zues, Dionysus Heracles and even Egyptian deities also found their way into Corinthian culture during this period.
In light of the myriad of religions and gods present in Corinth, it is not surprising to find a myriad of customs and practices that varied from time to time, place to place, and sect to sect. Not only were the customs themselves varied, but separate groups with shared customs still possessed different reasons for engaging in those customs. For instance, Jewish men covered their heads during worship to symbolize their guilt under the law, while certain Greek men covered their heads in accordance with the mystery cults that taught followers to cover their heads while engaging in religious sexual rites and ceremonies to preserve their anonymity. So certain Jews and certain Greeks both covered their heads, but for very different reasons.
Jewish men wore (and still do) head coverings, called talliths, as a symbol of guilt and shame before God. It was their way of showing that they were guilty under the law and their sin separated them from God. To this very day, the practice still stands in Jewish worship. Jewish women consistently covered their heads during this time, but throughout Jewish history there is evidence of women freely appearing without head coverings. But during this time, it would seem the majority of Jewish women absolutely kept their heads covered in worship services, in public, and even in their own homes, lest they face dire consequences (more on that later...)