God spoke to the woman (Eve) after the Fall (Genesis 3: 16) and He started with a discussion of her state during childbirth. There might have been some discomfort associated with the birth of a child in the original state into which the woman was created, but now that would be painful. Before the Fall the man was to have dominion over her and she would be comforted in that peaceful ,secure relationship. Now she would desire to usurp his leadership role.
Two Hebrew words are important for our understanding of the text: "Teshookataach" which means "to desire", and "Yemshall" which means "to rule". Both of these words appear in Genesis 3: 16 and again in Genesis 4: 7 and they have the same meaning in both verses. They indicate a desire to rule over something. In this case it is the woman who from the Fall onward has had a desire to rule over her husband. She will have a desire to control him and desire his headship. There is now a built-in conflict within the family. This came about in divine retribution because she chose to act independently from her husband and disobey God's Word. God says that He alone owns vengeance (Deuteronomy 32: 35a).
Her husband also would be a ruler over her. This does not mean a loving leadership that accompanies God's initial plan for marriage and the treatment toward her in general. His rule over her would be sinful and domineering. Later the man and the woman would have to master sin just like Cain (Genesis 4:7). Those who continued to turn away from God (like Adam and Eve did) would follow the sinful and natural inclination that God gave to the relationship. Man would dominate woman and she would resist and seek to usurp his rule. Before the Fall she was subordinate to him, but now in the fallen state God's plan for their hierarchy, their relationship would give way to competing dominance and resistance. God did provide for her though, but only to those who followed Him and kept His Word. God's plan is always best.
Because she led the first transgression (Genesis 3:6,13,16; II Corinthians 11:3; 1 Timothy 2:14) she would not have a leadership over men in the spiritual community in both Testaments. In the New Testament men are to love their wives as Christ loved the Church, He gave His life for it (Ephesians 5: 25). Additionally, she is to be subordinate to him in Christ (Ephesians 5: 22), which is a restoration of God's original plan for headship now found in the dispensation of the Church. It is only by God's grace and the Holy Spirit's leading the genuine believer that we can experience the marital relationship He intended. -- Dr. Daniel Woodhead (10/11)
Source: Woodhead, D.E. (2011) Commentary on Genesis.