This is the 5574th most frequent Russian word.
посвященное
"Devoted" or "dedicated."
In this sentence, 'посвященная' acts as a past participle in the nominative case, modifying 'книга' and giving information about the theme of the book.
Книга, посвященная истории России, стала бестселлером.
The book dedicated to the history of Russia became a bestseller.
Here, 'посвященную' is a participle describing 'скульптуру', in the accusative case due to the direct object reference.
На выставке я увидел скульптуру, посвященную героизму воинов.
At the exhibition, I saw a sculpture dedicated to the heroism of warriors.
In this example, 'посвящено' is a short-form past passive participle, agreeing with 'мероприятие', expressing a specialization of the event's focus.