means ‘reminiscence’ which is to tell a story that happened in the past. For example,
- 옛날에 알았던 사람인데 이름이 생각이 안 납니다. (=옛날에 알던(O))
I cannot remember his/her name who I used to know in the past.
- 작년에 자주 갔던 커피숍이 문을 닫았어요. (=자주 가던 = 자주 간 (O))
The coffee shop is closed that I often went last year.
- 한국에 살 때 자주 먹었던 음식이 뭐예요? (=자주 먹던=자주 먹은(O))
What was the food that you often ate when you lived in Korea?
- 예전에 많이 했던 게임이에요. (=많이 한 (O), =많이 하던(O))
It is a game that I played a lot before.
- 어제 봤던 영화 제목이 뭐예요? (=어제 본 (O))
What was the title of the movie that you watched yesterday?
- 어제 보던 영화 제목이 뭐예요? (=어제 본(O))
What was the title of the movie that you were watching yesterday?
- 집에 가던 길이었어요. (=가는 길(O), =갔던 길(X)) in progress
It was on the way to go home.
- 이곳은 제 남자 친구하고 제가 처음 만났던 곳이에요. (=처음 만난(O), =처음 만나던(X))
It was the place where I first met my boy friend.
- 예전에 한번 와 봤던 기억이 있어요. (=와 본(O), 와 보던(X))
I have a memory that I have been here before.
Usually -았/었/였던 and -던 are interchangeable, however if an action is finished (like sentence 7,8,9), they are not interchangeable. In this case, you can often see 처음, 한번.
Sentence 5,6 have different meaning. Sentence 5 is “What was the title of the movie that you watched yesterday?” while sentence 6 is “What was the title of the movie that you were watching yesterday?”.