What are the differences between men and women?

There are a very large number of traits that vary within the human population (or, for that matter, within the population of any species). The values of each of these traits, then, can be plotted in an n-dimensional space, where every individual occupies some position in that space according to their value for each varying trait. Plot the entire population of all humans in such a space, and you’ll get a cloud of points. That cloud is not spherical; it tends to be longer among some directions than others, due to some traits correlating with others. A principle axes analysis can point out which traits are correlated with others.

Sex is the name we give to one of the particularly high-ranking axes in this space. That is to say, there are a very large number of traits which are correlated in such a way that most people are close to one or another sub-clump in the space. The direction between those two sub-clumps is the gender axis. For instance, the people who are labeled “male” tend to have high testosterone, low estrogen, a penis, testicles, XY chromosomes, facial hair, higher height, higher strength, especially upper body strength, low-pitched voices, small breasts, etc., while the people who are labeled “female” tend to have the opposites of those traits. This does not mean that all men conform exactly to the standard of “male” (it’s a fuzzy cloud, after all), but most people are nonetheless significantly closer to one standard than to another.