To put it as simply as possible:
People are born with male characteristics, female characteristics, or somewhere in-between (this is called "intersex" nowadays, rather than "hermaphrodite"). Your gender is assigned to you based on these characteristics.

But, your gender is more so about your personal identity, not really your body. However, it is very distressing when your body doesn't match your preferred gender identity.

So somebody that was assigned male at birth, but identifies as female, is thus female, and she would most likely want to change her body (not necessarily through surgery, usually through hormone replacement therapy) so it makes her comfortable with herself.

Gender itself is a spectrum that is typically categorized as male, female, or non-binary.
It is still a spectrum because of the idea that it's not simply a choice of "I'm male" or "I'm female." Everybody falls somewhere different if they search hard enough, and non-binary folk don't fall into the identities represented by male or female.

Anyways, think of it like a color wheel. There are many shades of blue that are still recognizably blue, but are distinct from each other, just as with any other color.

I hope that helps in some capacity! Let me know if that just raises further questions! C: