A person's gender identity is just what it sounds like. It is the gender that they identify as or that they perceive themselves to be in spite of the gender assigned to them. Gender identity takes into account whether a person considers their body to be male and/or female and the many ideas their culture has about females and males.
The gender identify of cisgender females is woman and of males is man. Transgender people have a more challenging job. Common gender identities among trans people are transgender, transman, transwoman, man, woman, genderqueer, drag queen, and cross dresser.