Complementarity is the principle that certain creatures or things are meant to exist in pairs. They thrive or function better together than separately.
For example, a battery and a flashlight. The battery has potential to provide electricity, but that potential remains in reserve until it is inserted into the flashlight and the power switch is turned on. The flashlight has the potential to provide light, but without power it is useless.
Most religious people, along with many psychologists, believe that man and woman are complementary. The Bible notes that God made people male and female. (Genesis 1:27) It also recommends that a man and woman form a couple. (Genesis 2:24) It is not merely because God commands us to do this that men and women marry. Rather, it is because God made us in such a way that our lives are happier when we do this.