This is the 222nd most frequent Swedish word.
egna
"Egna" in Swedish means "own" (plural).
The word 'egna' here is used as a possessive adjective to indicate ownership of the books by the speaker.
Jag har mina egna böcker.
I have my own books.
In this context, 'egna' emphasizes the personal responsibility of handling the problems.
De måste ta hand om sina egna problem.
They must take care of their own problems.
Here, 'egna' stresses the individuality and uniqueness of the dreams as being specifically hers.