Many agree that Korea is probably home to the most Confucius society on the planet. Many social structures and hierarchical ideas breed from the Confucius ideal that education is of prime importance. As one Korean proverb goes: "It is better to teach your child one book, than to leave him a fortune."
As such, teachers in Korea are greatly respected and revered, and normally placed in the same category as other highly paid white collar job descriptions - Even more so than in the West.
Those who devote themselves to educating the younger generation are highly regarded by parents and the public in general. But that's where it stops, because, as I shall explain, your students will not always share the reverence their parents might have towards you. I've read elsewhere that "Teachers in Korea are treated with great respect by their students, and this extends equally to foreign teachers as well". But I have to disagree.
The fact that you're a foreigner means you, at least in the minds of your younger students, do not quite fit into the role of "Korean educator", and they tend to treat you very differently than they do a Korean counterpart. In their thinking, your eyes are simply to round, your face to gaunt (and small!), and your voice to strange to qualify you as a normal adult who should be treated with the same kind of honourable respect usually given to their Korean teachers.
I've had young kids, even in a formal school setting, treat me disrespectful, but not in the sense you might think. There's never any trace of resentment or rudeness, but rather an intense curiosity towards anything foreign (like yourself) to the point where you can end up feeling like a new toy being used and abused to see what sounds you can make and which dances you can perform.
Kids will scream at you, bombard you with "Hello how are you?" and run straight up to you with the weirdest questions ("Teacher you handsome, you are girlfriend?"). They'll treat you like the novelty and strange creature you are, in their eyes.
I've personally often found it difficult and frustrating when young children treat me this way (even though they don't mean any harm), but most other foreigners seem to handle it well. A disarming smile and attempt to engage the kids with honest answers is usually the best approach and you'll soon realise that they don't mean to be rude. They're just fascinated with your red hair or you tall figure.
All of this is of course truer of the younger kids, like those in Elementary school or Kindergarten. Older students undoubtedly share the same curiosity as their younger counterparts, but with age and wisdom, have learned to suppress it better.
Middle or High school students will often be able to express their fascination with you in a better way, since they have a more advanced grasp of English. Male teachers in middle and high schools are often on the receiving end of innocent and naive romantic inquiries and Valentine's cards from a flurry of giggling girls.
In short, if you've always had a hidden wish to experience the rock 'n roll lifestyle of being famous and turning heads wherever you go, your students in Korea will at least partly fulfil that wish.