There are well-known differences in brain structure, such as the portions of brain used for language. Women have an edge in verbal reasoning, while men in spatial.
Male IQ has more variability than female IQ, resulting in more men in both the top and bottom percentiles. This may explain why more men are executives, and why more men are homeless (that's just my suspicion). Studies have also found that male IQ is higher on average by (variously) 3-5 points. From my personal observations, men are more likely than women to focus intensively on one activity, to the exclusion of all others, like skateboarding, or surfing, or computer programming, or gaming.
Men weigh more than women, have more muscle mass, have 40-60% more upper body strength, and 25-30% lower body strength, though with training the gap narrows to 0-8% (so perhaps this difference is more cultural). Men outperform women in most athletic areas, though perhaps not in distance running. Women live years longer than men and have lower rates of mental illness.
Women and men earn equal pay when you control for the job worked, the hours worked, and the amount of experience. I believe a study showed that single male and female professionals with no dependents, equal time in the workforce, working equal hours, earned equal amounts. The pay gap arises because slightly fewer women work high-paying jobs, they work fewer hours per week / take more time off, and drop out of the workforce at higher rates (e.g. stay at home parent).
A good summary of research and sources are available in Wikipedia articles like "Sex differences in intelligence" and "Sex differences in psychology". Certainly do not take my word for any of this, and please correct me if I'm wrong.
Personally, I think we should make sure that every person is judged based on individual merit, and be encouraged and supported to pursue what they're interested in with no preconceptions. That's what equality means to me.