What is the relationship between sex and gender?

Sex refers to your Biology; do you have a penis or a vagina. Gender is socially constructed. Simply put, gender is a category that encompasses societies expectations for what is manly for a man and womanly for a woman (masculinity and femininity). Sex and gender are not immutable, for instance, it is possible to be transgender (born of one sex but identifying predominately or living as the opposite gender than your biological sex) or transsexual (born of one sex and then undergoing surgery to have your sex changed to the opposite sex).