In the past it might have been more-so for immigration purposes, but Korea is now a highly developed and thriving country (in fact, it is one of the most quickly developed nations in the world, look up Korea pre1970s and you will be amazed at how far Korea has come in such a short amount of time)- so while some might immigrate it's not necessarily out of necessity but just because they want to (/family, etc). Economy has nothing to do with it- Korea's economy is in tune with the U.S's.
These days many many young Koreans come to the U.S because of schooling- and the main focus? English English English. English is highly valuable in Korea and everyone learns it. To even get a decent job in Korea you're going to have to at least know English well enough to get a decent score of the TOEFL (English proficiency score) or a high score for a good job, etc... it's really, really, really important and why Korea is always seeking for Native English speaking teachers to teach in the schools/academy's of the country.
Hope that helps:)
I have lived in Korea and will be returning to be an English teacher this year. My boyfriend is Korean and I have a lot of Korean friends.