Korean culture could be characterized as group-oriented and hierarchical. A connection to another person makes one part of a larger group and this creates reciprocal obligations. Examples of connections that create a group would be: coming from the same hometown, attending or having graduated from the same school, university or college, working in the same company, family ties, common military service, or having the same occupation or profession.
It is very important to determine which party is the senior and which is the junior and seniority is generally based on age or job title. The Korean words to describe the senior and junior parties are "sun-bae" and "hoo-bae". There is no good translation into English because the concept is not really a part of Western culture. Koreans will typically say "my senior" and "my junior" when speaking English even though these expressions sound awkward to Western ears.
A senior is regarded sort of like an older brother or sister and is expected to provide support and guidance to juniors. A junior is like a younger brother or sister and is expected to show respect by speaking in a more respectful form of Korean.
Juniors and seniors can become close friends but depending on the circumstances, the heirarchical nature of the relationship can bring about a different dynamic than ordinary friendships in the West. Socializing is an important part of building a strong senior-junior relationship.
The senior can expect to spend more money on the relationship than he gets spent on him by his junior. And in some cases, the junior can expect to spend considerable time carrying out tasks for his senior with no or little direct reward. It might appear unfair or unbalanced, but there is give and take by both parties, and every junior will be a senior to someone more junior to him and vice versa.
Like any human relationship, there exists the potential for abuse. Some seniors will take advantage of their juniors and ask them to do an unreasonably large number of tasks, pressure them into doing things they really don’t want to do, or get on a power trip. The senior-junior relationship can be a great one but unfortunately it sometimes does go wrong.
It is unlikely that a foreigner would be expected to become the senior to a Korean in Korea but this may be expected outside Korea. This would just involve providing some assistance, guidance and non-financial support, which most people would be willing to provide anyway. A Korean would probably feel obligated to act as a senior towards a younger foreigner, particularly in Korea. You can feel comfortable about asking for guidance and non-financial support from a senior Korean and recognizing this junior-senior relationship can even deepen the friendship by showing a sensitivity to Korean culture.
If you find yourself in a senior-junior relationship, you can expect that you may be called on from time to time to carry out tasks without compensation in line with your role as the junior. It will help the relationship if you carry out these tasks. Tasks for a foreigner would typically involve helping with English or making use of knowledge or contacts in the home country. Beware of people seeking to take advantage of you. Teaching or proofreading English on an ongoing basis for free or being pressured to take a position is unreasonable and you should refuse such requests, although doing so with grace is always advisable.