Korean culture is more conservative than that of western countries. Dressing tastefully and appropriately is greatly appreciated by your Korean colleagues. Moreover, semi-professional attire will help gain the respect of your students.
By no means are you required to wear a suit or a dress but having one for special occasions is a good idea.
Men should wear button-down shirts and nice pants. Wearing a collared shirt with a tie is good way to start out and show respect.
Women should avoid low-cut or overly tight clothes but nice pants are fine.
Earrings and piercings on men are not acceptable in Korean schools. The schools are fairly conservative, and it is a good idea for you to be so as well.