This is the 10349th most frequent Polish word.
ciekawą
"Interesting" (feminine singular form in accusative or instrumental case).
The word 'ciekawą' is used here as an adjective in the accusative case to describe a feminine noun 'książkę', showing that the book is interesting.
Czytałem ciekawą książkę wczoraj wieczorem.
I read an interesting book last night.
Here, 'ciekawą' functions as an adjective in the instrumental case describing the feminine noun 'możliwością', indicating that the opportunity is interesting.
Udział w tej konferencji wydaje się być ciekawą możliwością.
Attending this conference seems to be an interesting opportunity.
In this context, 'ciekawą' is an adjective in the instrumental case modifying the feminine noun 'historią', highlighting that the life story is considered interesting.