러 떠나다

set off to do something

"-(으)러" marks the purpose of a trip and 떠나다 is "depart, set off", so together: left in order to do X. The scale ranges from a real journey — left for Samoa for the Commonwealth meeting, left for the US on promotion, a nationwide tour to meet that success story — to playful captions about someone leaving the room: off to do his day job, off to keep a prior engagement, off to have good dreams. Compare 러 가다 "go to do"; 떠나다 adds the sense of leaving here behind.