Korean may not be one of those languages which marks gender grammatically, it is a language where there are clear but subtle differences between men and women.
Let's first talk about the role of Korean women in society. There are some societies where women dominate social life (notably in the Pacific), some societies where women are increasingly vocal about changing their role in society (in most modernized cities around the world) and some societies where women are reduced to "minor" roles in society. Anthropologists argue that whatever the society, no society is necessarily "better".
Korea has experience a dramatic change, going from an agriculture society to an industrialized society within a span of 20-30 years. Alvin Toefler, a sociologist who is unheard of in western societies but very popular among societies which experienced such abrupt and dramatic change, coined the term "future shock", where people within the same society are disoriented and do not recognize the society they live in after it experienced dramatic changes within a brief amount of time.
What does this mean for Korean women? Korean women used to have the traditional roles of bringing up children and taking care of house chores. Women did not interact with other men and women working in companies along with men was considered "inconceivable" until the 1970s. Until then, most college students were men and college was considered an improper place for women to be. Women did attend high school, but without having college in mind. Women married some time after graduating from college, and marriages were in most cases arranged, as women did not have the opportunity to meet other men. Men and women were segregated from junior high school onwards, and in some cases, from elementary school. I am no fan of the Confucian explanation of these gender roles, and my view on this is that socio-biological elements played a crucial role, though I will not elaborate this here.
Women were considered inferior to men in the sense that they had to show respect to men, and men had to protect them. Note that words like nuna and oppa were strictly restricted to the family circle and were not used for people with whom no blood ties were established.
This is when future shock came in. Korean economy became industrialized, it was easier to find food, and women were needed in the workforce. Women entered the workforce, but were still considered inferior to men. Though today there is a significant number of congresswomen, CEOs (yes there are!), professors etc., one should note that they almost exclusively work with other women and limit their interactions with men. Men still won't take orders from women, won't listen to them and will only accept orders from a male boss. Though things changed in 30 years, the older generation of men which witnessed women confined in their role as "mothers" is still alive, therefore it may take some time for women to be considered equals with men.
When it comes to language, women and men differ in their prescriptive use of "polite speech". While women directly or indirectly invite those younger than them (men and women) to use "plain speech" (반말) as long as the women are not married, men will tend to impose "polite speech" to those who are younger than them. Note however that both men and women tend to use "polite speech" with married women.
Children may use "plain speech" with their mothers in public, however, while many children will use "plain speech" with their father in the private sphere, they will use "polite speech" in public.
Women also differ in the sense that they tend to view conversations from a more "equal" perspective and tend to agree on the fact that both should "lead" the conversation. This is not true of married women. Men, in contrast, tend to think that there should be a "leader" in the conversation. Note that, regardless of age, men tend to lead conversations even when they are with older women, but not with married women.
Finally, at the workplace, women tend to mix "polite speech" and "plain speech" with their subordinates. Women will tend to use polite speech when they give orders to their subordinates ('해 주세요') whereas men will exclusively use plain speech with subordinates.
Finally, there are some differences in the way men and women formulate their sentences:
Women: Tend to be more careful when they use "polite speech" with men, tend to use longer sentences, to color their speech with more "hesitation" words when asking for a favor (저 있잖아...), tend to speak with more intonations and their voice tends to be more nasal, tend to formulate questions rather than make assertions, use body language a lot when they talk.
Married women: Sentences tend to be shorter, careful with polite speech when speaking to men, use very few "hesitation" words, tend to refute what younger people will tell them (often use the phrase "그개 아나라" after younger people make a statement), tend not to look at men when they talk to them, little body language.
Men: Less careful with polite speech when talking to women, very careful with polite speech when talking to superiors, use few "hesitation" words, make more assertions and ask fewer questions, very short sentences, body language is still make little use of hands or body when talking, though they do tend to touch their hair a lot, tend to giggle while they speak when speaking to hierarchical superiors or women.
Upper class men: speak with long sentences, use "plain" speech (반말) with virtually every group, vowels tend to be longer than other groups, smile a lot but laugh very little when they talk, few "hesitation" words, constant interruptions, constant refutation of what the other person says (using 그개 아니라), very little body language, higher voice pitch than other groups.