Don't you have to know the korean language before teaching something to korean people?
no. They are taught english throughout their schooling and usually foreigners who go over to teach are teaching kids who have a year or two of classes or adults and don't have to speak a word of korean
the schools basically hire you as a marketing thing. It's common for parents to send their kids to things private institutions called 'hagwon' after their formal education and they're basically little micro-schools that offer additional classes(english, computers, music, math, etc.). It looks really good if they've got a native english speaker on staff and since there's a ton of them in any given area, it's like a little leg up on the competition.