A lot of times this really is legit, though. Learning English is really important to Koreans (because, you know, a lot of them like to come over here), and the best people for them to learn from are native speakers.

The problem is going over there with no connections and not knowing the language, etc. If the job suddenly goes away after you've gotten settled (which also sometimes happens with these), you could end up in a really bad situation. The best case scenario for getting a job like this would be through Koreans here that you know and trust. Of course, that's not an option for everybody, and you should consider just how risky it could be to be stuck in a foreign country with no friends, no job, and no money and decide if that's something you could prepare for.

You should investigate things like this as much as you can. If you find out that this offer seems to pay way more than other ones, for instance, then Derris could be right.