There has been much debate in recent times regarding the meaning of this. Some argue that it refers to a desire for woman to have children and become a mother. In order for this to happen, a woman needs a husband and this need for her marriage partner will then put her husband in a position from which he can dominate and rule over her.1
Traditionally, however, it has been understood that instead of being a helper to her husband (Genesis 2:18), the woman now seeks to control her husband. The same word for desire found in this verse is used in a negative sense in Genesis 4:7. Thus, as a result of the Fall, the woman’s desire for her husband is negative (controlling). However, she will not succeed in her plans for domination because God has ordained man to exercise the leadership function in the home.2
16 To the woman he said, “I will surely multiply your pain in childbearing; in pain you shall bring forth children. Your desire shall be for your husband, and he shall rule over you.”