I'm not familiar with the Korean context, but I'm guessing it's not too far from the Chinese "sifu" - which is also often translated as "master", but it's moreso "mentor" or "teacher". Someone who is skilled in a trade and is teaching someone their skills
Edit: there's also usually an element of this person as a bit of a surrogate parent. A lot of the service the apprentice does for this person will have a tone of filial piety