The clausal connective ~는 /(으)ㄴ데 is used to provide background information for the main clause. Consider the following example:

한국어를 공부하는데 아주 재미있어요.

“(I) study Korean, and (it) is very interesting.”

In this example, the first clause 한국어를 공부하다 “(I) study Korean” is the background information for the main clause 재미있다 “(it) is interesting.” Here are more examples:

오늘 밤 추운데 밖에 나가지 마세요.

“(It) is cold tonight, so do not go outside.”

점심 때가 됐는데 어디 가서 뭔가 먹어요.

“(It) has become lunchtime, so (let’s) go somewhere and eat something.”

이번 주는 약속이 있는데 다음 주가 어때요?

“As for this week, (I) have an appointment, so how about next week?”

내일까지 일을 마쳐야 하는데 하나도 안 했어.

“(I) have to finish the work by tomorrow, but (I) have not done anything.”

오늘은 바쁜데 내일 만나자.

“As for today, (I) am busy, so (let’s) meet tomorrow.”