"But I want you to understand that Christ is the head of every man, and the man is the head of a woman, and God is the head of Christ." (1 Cor. 11:3).
In the Jewish and Christian culture when the Bible was written, there was a concept called "Federal Headship." This means that the male is the one who represents his descendants. Proof of this can be found in Heb. 7:8-10, "And in this case mortal men receive tithes, but in that case one receives them, of whom it is witnessed that he lives on. 9 And, so to speak, through Abraham even Levi, who received tithes, paid tithes, 10 for he was still in the loins of his father when Melchizedek met him." Notice that it says that Levi paid tithes while still in the loins of his father Abraham. How did he do this? By proxy since Abraham, his distant "father" represented him.
Likewise we see the concept of Federal Headship in the fall. It was Eve who first sinned. But sin entered the world through Adam--not through Eve. Romans 5:12 says, "Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned." This is because Adam represented humanity and creation. When Adam fell, we fell. This is why it says, " . . . in Adam all die." (1 Cor. 15:22). Also, Romans 5:15 says, "For if by the transgression of the one [Adam] the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many."
Alright, so this brings us to the woman. Again notice that it says in Gen. 2:24, "For this cause a man shall leave his father and his mother, and shall cleave to his wife; and they shall become one flesh." When a man and woman get married, they become on flesh. There is a unity between them. But, it is the man who is the head of the family which is why it says that the man is the head of the woman.
Some may think that this was a cultural notion that snuck into the Bible. But Paul makes it clear that the headship is related to the created order:
"For man does not originate from woman, but woman from man; 9 for indeed man was not created for the woman's sake, but woman for the man's sake. 10 Therefore the woman ought to have a symbol of authority on her head, because of the angels." (1 Cor. 11:8-10).
It was because Eve listened to the devil that the issue of order and hierarchy in the marriage relationship has had to be raised and explained.
"I will greatly multiply your pain in childbirth. In pain you shall bring forth children; yet your desire shall be for your husband, and he shall rule over you." (Gen. 3:16).
This headship is not about having the upper hand, nor is it to mean that a woman has no rights or is a second-class citizen. On the contrary, God tells the husband some very serious commands:
"Husbands, love your wives, just as Christ also loved the church and gave Himself up for her; 26 that He might sanctify her, having cleansed her by the washing of water with the Word, 27 that He might present to Himself the church in all her glory, having no spot or wrinkle or any such thing; but that she should be holy and blameless." (Eph. 5:25-27).
Finally, the headship issue is an issue of order--not of who is better or more important. The husband is the head of the wife in the family, and he has the responsibility of guiding his family to a closer relationship with the Lord. God will require it of him on the day when all our deeds are judged by God.