맺히다 means "get formed over time like through accumulation, condensation, etc"
가슴에 맺히다 = got formed in the heart / settled (deposited) in the heart
It can be used for many different things.
- (눈물, 땀, 이슬이) 맺히다. - form/gather tear, sweat, dew, etc.
- 피가 맺히다. be red with blood; be shot with blood.
- 한이 맺히다. accumulate/harbor deep resentment (over a long period).
- 열매가 맺히다. bear fruits.
Because of its nice connotation it is used a lot in poems and song lyrics.
All the examples below are from songs which you can easily locate on YouTube or song lyrics sites, if you want to see the rest of the lines.
긴 밤 지새우고 플잎마다 맺힌.. (김민기 "아침이슬")
=> Hanging onto each leaf after a long night...
아 피맺힌 그 기다림도.. (노찾사 "그날이 오면")
=> And the long bloodshot wait too.. (피맺힌 = 피가 맺힌)
별빛 같은 너의 눈망울에 이슬방울 맺힐 때.. (신촌블루스 "아쉬움")
=> As the dewdrops start to form in your starry eyes
그리워 마디마디 이끼 되어 맺혔네. ("비목" - 가곡)
=> The longing turned into moss to eat into every knot.
원한 맺힌 마음에 잘못 생각해.. (문주란 "동숙의 노래")
=> Misguided by a blinding resentment..