What are the differences between men and women that are proven by science?Men are, on average, taller than women. This is an easy fact to measure and demonstrate. That does not imply any particular man is taller than any particular woman. It just means that if you select a male and female at random from the entire population the chance of the male being taller than the female is greater than 50%.
They are also often physically stronger although this is somewhat harder to measure (what kind of body strength are we talking about?).
These physical traits don't have as much meaning in the modern economy as they used to. Regardless they are fairly easy to measure on a personal level. It would be blatancy ridiculous to deny six foot five woman a job which required you to be tall for being too short because "women are short".
Biological males and females have different reproductive organs. Men cannot bear children. This can get a bit confused when we talk about the portion of the population which has more than 2 sex chromosomes (X or Y chromosomes). Some people are born with ambiguous genitalia.
As far as the mental stuff goes the data gets very fluffy. Its incredibly hard to tell what could be an innate biological difference and what is caused by society. I suspect that there are more women in America who like the color pink than men. I also suspect this has absolutely nothing to do with biology. Men and Women have near identical average IQ Scores. I don't think there is any good reason to think that the mental capacities of men and women are very different. Higher reasoning is a skill that is highly useful to survival for both genders. I doubt evolution would favor intelligence in men but not in women.
In general people should be treated equally unless there is very, very compelling evidence why they should not be. The evidence that women are mentally very different from men is very shaky.