This is the 3337th most frequent Korean word.
남아있는
"Remaining" or "left."
In this sentence, '남아있는' is used as an adjective modifying '책' (book), indicating that the book is the one that remains or is left behind.
책상 위에 남아있는 책이 내 것입니다.
The book left on the desk is mine.
Here, '남아있는' describes '낙엽들' (fallen leaves), expressing that these leaves are still present.
공원에는 아직 남아있는 낙엽들이 많습니다.
There are still many fallen leaves remaining in the park.
In this example, '남아있는' pertains to '기억' (memory), symbolizing that the memory persists or continues in one's heart.