This is the 1952nd most frequent Polish word.
będących
"Being" or "which are" (plural, genitive or locative form).
In this sentence, 'będące' describes the books (książki), explaining their state of being located on the table.
Książki będące na stole należą do mnie.
The books being on the table belong to me.
Here, 'będącymi' agrees with 'osobami', specifying they are experts.
Spotkaliśmy się z osobami będącymi ekspertami w tej dziedzinie.
We met with people being experts in this field.
In this example, 'będące' refers to the children (dzieci), signifying they are under the teacher's care.