Gender identity is your own internal sense of your gender — woman, man, both, neither, or somewhere else — whether or not it matches the sex you were assigned at birth.
Everyone has a gender identity. It's the answer your own head gives to the question "what am I?", running quietly in the background whether you ever stop to think about it or not. For most people it lines up with the sex a doctor announced at birth, so it stays invisible — like a track you only notice when it cuts out. For trans and nonbinary people it doesn't line up, and that mismatch is the whole point. Either way it's internal: nobody can read your gender identity off your body, your clothes, or who you go home with.
Three things get shoved into one box and they really shouldn't. Gender identity is who you are. Gender expression is how you broadcast it — haircut, clothes, voice, the way you take up a room. Sexual orientation is who you want. They move independently: a woman can be butch and straight, a man can be femme and gay, a nonbinary person can be into everyone or no one. Sex assigned at birth is a fourth thing — a label handed to you before you could talk. Confusing them is how the bad takes get made.
On the floor this is just basic respect. Someone's gender is whatever they tell you it is, full stop — you don't get a vote, and you don't need a medical file to believe them. The kink and queer scenes have run on self-determination for decades, long before the word "identity" turned up in anyone's paperwork. You call people what they ask to be called, you use the pronouns they hand you, and you get on with the actually interesting part of the night.