Complementarianism is the view that males and females complement each other in their different roles and duties. In the context of Christianity, men are to be leaders in the church and the home where women are not. Likewise, women are to assist the husband in raising children and expanding the kingdom of God.
Christian complementarianism does not see women as inferior or men as superior. Instead, it sees them as being identical in nature but different in function and role. For example, women are to bear children where men are not. This obvious biological difference is a complementarian necessity within the family. Likewise, men are to lead their families with Godly direction, and the women are to support their husbands in their leadership.
Therefore, in complementarianism, when we look at what the Bible says about the difference of roles in leadership in the church, we find that women are not to teach or exercise authority over men (1 Tim. 2:12) based upon the created order (1 Tim. 2:13). Likewise, elders are to be male (1 Tim. 3:2, Titus 1:6). This difference of authoritative structure is not based on culture but on the fact that Adam was created first.