On a basic biological level, being a woman means having two X chromosomes and being a man means having one X and one Y chromosome. This difference in DNA leads to different primary sexual characteristics. Women have ovaries, a vagina, and a uterus and are capable of bearing children and lactating. Men lack ovaries and a uterus, and cannot bear children, but do contribute sperm to the process of sexual reproduction. Women generally have higher body fat and lower upper body strength than men, and tend to live slightly longer than men do.
Many societies assign different gender roles to men and women. These are purely socially constructed or what gender theorists call "performative", in that they are arbitrary conventions followed by particular social groups. They vary depending on the specific society in question.