There's so much to do in this airport, you could spend a holiday there.
Get an introduction to Korean art and culture at the airport's Korean Culture Museum on 4F concourse in Terminal 1, where you can try craft experiences and learn to write your name in Hangeul. Or take a stroll around the traditional houses in Culture Street in the public area of Terminal 1. There are 7 mini-gardens dotted around the airport and you can even take in a movie at the CGV theaters near the airport's Transportation Center.