What makes someone a man or a woman?

As you all know

there is this story

“Caster Semenya, the South African sprinter who won the women’s 800 metres at last month’s World Athletics Championships in Berlin, is a hermaphrodite, according to several published reports.

According to the reports, the International Association of Athletics Federations was preparing to disqualify Semenya, 18, from future events after gender tests uncovered evidence that she has no womb or ovaries, and carries both male and female sexual organs. ”

I am interested in talking about transgender and transsexual as well, whether if people feel that it is another form of intersex condition or a mental illness.