This started as a Trans & Gender 101 article but I realized it's closer to a 300 or 400 level concept. While no one agrees that sex is basically the biological aspect of being female or male and for cisgender, non-intersex people that's fully adequate. But when we have advanced conversations about sex and gender we face the disadvantage of having language only meant to accommodate cisgender, non-intersex people. When transgender and intersex people come into the picture, we are faced with asking, "how do we talk about people who are not 100% female or 100% male? What exactly makes someone male or female?"

Before reading this, it may be helpful to understand what I think of words and definitions. I discuss this in Semantics. I stress that I do not think there is one true definition and many false definitions. Rather, some definitions are more useful than others.

Ancient definition

Penis equals male. Absence of a  penis is female. Most people are still using this very old definition. Note the sexism where males have more than females; a vagina is seen not a possession but a lack of possession.

Genes-only definition

XY is male and XX is female. Other karyotypes are ignored or don't exist. I only hear this definition when someone in the context of trans issues where the speaker wants to prove no one can change their sex. See Objection: Sex Cannot Change for a treatment of this definition.

Transexual & Intersex definition

Sex is equivalent to gender identity regardless of the rest of the body. If your brain is female, nothing else matters. Arguably, this is more a philosophical view that gender is more valuable than sex than it is a scientific statement. That's fine. Note that many transexuals don't believe this, but my impression is most do.

Psychological definition

The biology associated with what is commonly considered female and male. The female includes XX chromosomes, vagina, clitoris, uterus, labia, breasts, wide hips, high voice, curves, mainly estrogen, and little testosterone. The male includes XY chromosomes, penis, testicles, wide shoulders, facial hair, deep voice, adam's apple, mainly testosterone, little and estrogen. I think this definition is useful because it incorporates all the following definitions as well as including historical and cross cultural understandings of sex. This defintion is also one of the best for intersex concepts.

Wholistic definition

Sex is defined the same as the psych definition, but gender identity, because the brain is biological, is an additional component. I like this definition most because it incorporates everything.

Reproductive definition

The physical property of a biological creature in regards to its role of reproduction. In a species, the creature responsible for creating offspring is female. A creature donating genetic material to the female is male. A creature who acts without a male to reproduce is an asexual female.

Obstetrician definition

When an infant is delivered, the obstetrician declares the sex based on the size of the clitoris/penis. (I believe the size is 1.5cm, but I can't find a source to back me up.) Even if prior chromosomal analysis has shown the child is intersex, most states require the doctor to ignore this and use genitals only.