TTMIK has a very good lesson on this in Level 7 Lesson 28. I suggest using that as a source of reference as well. I will supplement their lesson with some specific examples to highlight. To quote their definition:
- Noun + -(이)라는 것
- What I call “Noun” is…
- (I think that) “Noun” is…
- Comes from the construction (이)라고 하는 것
- Verb + -(ㄴ/는)다는 것
- “The thing that is called + Verb” and it is used to express what you think the definition or nature of a certain/state/verb
- Comes from the construction -(ㄴ/는)다고 하는 것
Both patterns take the form of the indirect quotation pattern (이)라고 하다 and (ㄴ/는)다고 하다. So literally you could translate it to being the “Noun” that is called and the “Verb” that is called. This literal translation of the noun structure is quite close whilst the verb translation needs more explanation.
In the noun case you can form sentences like
- ‘건설하다’라는 단어는 ‘짓다’와 비슷한 뜻이 들어있어요? Does the word (called or said to be) 건설하다 have a similar meaning to 짓다?
- ‘신뢰’라는 것은 어렵게 쌓이는 것이지만 쉽게 파괴할 수 있어요. (The thing called or said to be) trust is something that is difficult to build up but easily destroyed.
- “핵무기”라는 단어가 무슨 뜻이에요? A very useful sentence pattern when you want to ask a someone what does this word mean
In the first two instances you could have said ‘건설하다’는 ‘짓다’와 비슷한 뜻이 들어있어요? and 신뢰는 어렵게 쌓이는 것이지만 쉽게 파괴할 수 있어요. But by using this grammar you put a lot more emphasis on the noun. It can have a philosophical nuance to it if you say 사랑이라는 것 for example.
In the verb case you can form sentences like
- 네가 빵을 밥보다 좋아한다는 걸 나는 이해하지 못 해. I don’t understand how you like bread more than rice. Here the entire first clause has been transformed into an object via the 좋아한다(고 하)는 걸 construction. The clause translates loosely to “the fact”, “the notion”, “the idea” that (says) you like bread more than rice. The second clause is a verb that acts on the first clause (object). The verb here is 이해하지 못 해.
- 네가 어제 신발을 몰래 샀다는 걸 나 알아. I know that you secretly bought a pair of shoes yesterday. Like the first example, the first clause here has been transformed into an object via the 샀다(고 하)는 걸, and translates loosely to “the fact” that (says) you bought a pair of shoes secretly. 걸 isn’t precisely “fact” but you could actually replace it with 사실 to make it literally mean fact, but it is not necessary.
- 신문에서 당신이 외국에 간다는 것을 알았다. I found out from the newspaper that you’re going overseas.
When I learnt this grammar I was confused between this and 는것. If the difference is clear to you, you can stop here.
-(ㄴ/는)다는 것 vs (ㄴ/는)것
- 네가 어제 신발을 몰래 샀다는 걸 나 알아
- 네가 어제 신발을 몰래 산 걸 나 알아
The second sentence doesn’t make sense. 몰래 산 걸 means the thing you bought secretly. But if another object (신반을) is put in front of that, it turns “I know the thing that secretly bought the shoe.” And the 네가 at the front doesn’t make sense anymore.
Sometimes the two grammar can have a similar meaning.
- 건강에 좋다는 약
- 건장에 좋은 약
The first one emphasises “the medicine that is (said to be) good for health”. The second one simply means “the medicine that is good for health”.