This is the 2673rd most frequent Polish word.
będącej
"Being" (feminine, singular, genitive or locative form).
The word "będąca" is used as a present participle form of "być" (to be), describing the book's state of being in the library.
Ta książka, będąca w mojej bibliotece, jest bardzo interesująca.
This book, being in my library, is very interesting.
Here, "będącej" describes the state of the person specifically in relation to being aboard the ship.
Historia dotycząca osoby będącej na pokładzie statku była poruszająca.
The story concerning a person being aboard the ship was moving.
In this context, "będące" is used to describe the picture's state of being located on the wall.