Okay, some background on this. As a child, I was very unclear on what the differences were between boys and girls. I knew I was a boy, and that girls dressed differently and had different hair, but that was it. I was never under any illusions of girls being weaker than boys or behaving differently or anything; I grew up playing SNES games with my female cousin who was way better than me. I didn't know the two sexes had different private parts until I was 7 and read it in a health book. After that, I figured that was it; gender referred only to body parts and nothing else made a difference; people could be as masculine or feminine as they liked and it wouldn't matter. I remember having some odd fantasies of being a girl then but generally felt that didn't matter. I was a guy with an active imagination, that was all. Now, of course, after encountering enough trans people, my views shifted again, but to what I am not sure. It's clear to me now that body parts don't actually define gender, but I don't believe personality and thought processes do either; and after all, feminine trans men and masculine trans women exist too. I ended up wondering about my own identity in all that too and having no method by which to determine it, eventually just settling on living life as before for lack of a better option. So this brings me to the question at hand: If gender is not body parts and it is not personality, what exactly is gender and how does one define it?
It's a mix of who you are physically and mentally, mixed with a kind of social status - not heirarchal, but rather where a stronger connection is. Those are the fewest words I can think of to put together a definition. Gender itself is a very complicated subject, even when diving into it scientifically. There are so many moving parts to what makes up the brain and how it works. This is probably the main reason why the T is included in LGBT - All we're experiencing is the way our own brains function in tandem with our bodies.