There are three basic kinds of university jobs that you can get in South Korea and the vast majority of job advertisements you see will be for one of these positions.
4-Year University Your job will often consist of teaching mandatory Freshman (and sometimes Sophomore) English courses. Schools vary in how they administer this, but it can involve one 3-hour per week course during either the student's first or second semester, or it could involve something like four 1-hour per week courses over the first two years of a student's program. You will sometimes be able to teach other classes like writing, presentations, or business English to students in majors like business, airline business, tourism or English. It really depends on the university. Student English levels range from almost fluent to very low. All of these classes involve designing a syllabus, administering tests and homework, and giving final grades.
Community College These institutions offer two-year programs in fields like hair-styling, security or cooking. The students are still required to take English courses and will likely be extremely low-level and have almost no motivation to learn English. There is usually no opportunity to teach anything besides basic conversation at these places. This job is similar to the one above in that you will have to design a syllabus, administer tests and homework and give final grades.
Unigwon These are hybrid “university + hagwon” positions, which are located on university campuses. You will teach mostly university students and some adults from the wider community, but quite likely some children as well (if not mentioned explicitly in the job advertisement, you should ask about this in the interview). None of your classes will be for official credit so there are no tests or grades and you will teach things like basic conversation or run English discussion clubs. Your students will often be quite motivated because they have chosen to be there, unlike the previous two positions where students attend your classes because they must fulfill academic requirements.