A / V + 했던 is used to reflect on a former state or action in the past. 던 can be used in an almost identical way without the past tense modifier, but 했던 gives a clearer expression of completeness and experience:
예뻤던 여자가 요즘은 항상 피곤해 보여요.
The woman who was once pretty always looks tired these days.
(She was pretty but she’s definitely not anymore.)
고등학교를 다녔을 때 친구가 키가 작었던 요즘 키가 너무 커요.
When we were in high school, my friend was short but these days he’s very tall.
(He was short but that’s not the case now: he’s very tall.)
비쌌었던 옷을 세일기간 동안에 저렴하게 살 수 있어요.
You can buy expensive clothes for less during the sale period.
(They were expensive, but you can buy them now because they are on sale, and therefore cheaper.)
만든 음식이 생각했던 것 보다 더 맛있었어요.
The food I made tasted better than I thought it would.
(I had been imagining food that tastes bad but in fact that wasn’t the case.)