In an agricultural Korean society marriage used to be about having children who would work in farms. Koreans chose healthy women who could bear healthy children, that is, women with fat (because fat helps ovulation, therefore lack of fat causes problems with ovulation, menstrual disorders and eventually infertility) and strong women who could handle everyday chores. But with the advent of modernity things changed.
While in the past families played a critical role on who their children would marry, the role is decreasing. Let's have a look at the criteria Koreans look at when they look for potential spouses:
-Physical features ("beauty"): In Korean society, like in most modern societies, a spouse is a reflection of who a person is and tells more about a person than anything else. Spouses need to be slender or thin - a sign that they control their desires to eat and rest, a sign of being active - and needs to have "western features": "big eyes" (compared to average Koreans), "a bridge at the top of the nose", "double eyelids (the famous ssangkopeul)", an oval face (most Koreans have round faces), a "small face" (Koreans tend to have more voluminous faces than Westerners)... any feature that is common among Western people.
The reason: Koreans view westerners as a symbol of economic wealth, and want those wealthy westerners to have a positive impression of their spouses, therefore any physical feature that westerners don't have may be viewed as "deviant" by westerners, and westerners may therefore have a negative appreciation of their spouse. In Korea, it is out of the question to marry a person with any form of handicap, including Albinos, people with any form of skin disease or any other physical handicap.
-Family background: Family ties are very strong in Korea and families are very interdependent: parents give money to their children as long as they can afford to and regardless of age, and children are expected to give money to their parents. Parents therefore don't want their children to marry people with families that have a significantly lower income as theirs, as they may consider that the person is marrying for the sole purpose of money and inheritance. Families want their children to marry people who will contribute financially in some way to the family.
-Educational background: belonging to a university means belonging to a group. In Korea, alumni associations are very active because of the very strict social rules on networking. Being from a university means having access to numerous connections which will help a person develop economically (in terms of business) and in practical issues, such as when help is needed in case of emergency. Therefore both men and women are expected to have strong connections.
Since historically women from Ewha Women's University have tended to marry men from Seoul National University, both prestigious universities, women from Ewha tend to have strong connections with their alumni who married men from SNU. Ewha is a prestigious university for women for that particular reason, SNU is always a favorite, Korea and Yonsei are acceptable. Note that while graduate school in the United States is always appreciated, people tend to prefer marrying people who attended some form of college in Korea.
Job: Though money is not always important, women tend to prefer marrying men with promising jobs or even men attending promising universities that will lead them to getting a promising job. Though lawyers and doctors tend not to make a lot of money when they start their careers, they tend to have the reputation of making money as they advance in their careers. Businessmen, people who work in the broadcasting industry and professors are also considered prestigious careers.
Note however that men never marry women with careers, or ask them to put an end to their career after marriage. Why? The most common answer to this question is that women are expected to take care of their children, but I would add that there is a social taboo on women working at higher or equal positions than their husbands. In any case, Korean society accepts the fact that no woman should make more money, or even threaten to make more money than her husband, because society accepts the fact that men should provide economic comfort to their wives. The reason I'm saying this is that men who marry secretaries or flight attendants usually don't ask them to quit their jobs, even after they have children. But men who marry singers, actresses or any high income job do ask their wives to quit.