The gender binary is a system containing only 2 genders, man and woman. These 2 genders correspond to the sexes male and female, and the system tends to enforce the gender roles corresponding to each as well. Most of the world organizes itself based on the binary; you can see it appear in the form of gendered restrooms, sports teams, and certain schools. Although many people consider the binary genders to be the only genders, there are people who have a gender outside the binary. These non-binary individuals experience systematic exclusion under this system.
Men and women can be transgender, transsexual, cisgender, cissexual, or any combination thereof. They should not be confused with the sexes male and female, although they can be related. Men and women can have a wide range of gender expressions, sexual orientations, and romantic orientations. It's incorrect to assume that a man is automatically masculine and a woman is automatically feminine.