V + 고 나서 puts two events in sequence, with the second event occurring after the completion of the first:
밥을 먹고 나서 집에 갔어요.
After eating a meal I went home.
수업 끝나고 나서 뭐 할 거예요?
After class finishes, what will you do?
서울에 도착하고 나서 저는 옷을 사러 백화점에 갔어요.
After arriving in Seoul, I went to the department store to buy clothes.
하루 종일 공부하고 나서 책을 버리고 싶었어요.
After studying all day I wanted to throw my books away.