Quite simply, cognition refers to thinking. There are the obvious applications of conscious reasoning—doing taxes, playing chess, deconstructing Macbeth—but thought takes many subtler forms, such as interpreting sensory input, guiding physical actions, and empathizing with others.
In the old days, it was simple: Men hunted and women raised the kids. Then we moved out of caves, invented gender studies, and learned a thing or tow about genetics. Now nothing is clear cut. While social and biological analyses of gender offend some, they have freed others to finally feel comfortable in their own skin.