This is the 6315th most frequent Korean word.
싶었던
"싶었던" means "wanted to" or "had wanted to."
'싶었던' in this sentence is used to indicate a past desire related to the preceding verb '가고', expressing 'wanted to go'.
내가 가고 싶었던 장소는 산이다.
The place I wanted to go to is the mountain.
'싶었던' serves here to reflect a past desire to learn the specified song, paired with '배우고'.
그동안 배우고 싶었던 노래를 드디어 연습할 수 있게 되었어요.
I finally got the chance to practice the song I had wanted to learn.
'싶었던' here is used to communicate a recalled past desire or feeling of wanting to meet someone, connected to '다시 만나고'.