Complementarianism is the view that males and females have different roles to play but complement each other. They each have a distinctive purpose.
Within the creation narrative, there is a very clear account of male headship—Adam was created first, and then Eve was created out of Adam. Paul makes a great deal of that in his own theology, particularly in 1 Corinthians. In the creation account, you have the principle that male and female are equal in terms of their being, in terms of ontology. Both bear the image of God, but one is submissive to the other. You see this in the manner of Adam and Eve’s creation. Furthermore, the manner in which Adam is held responsible for what essentially was Eve’s sin is also part of that complementarian argument.