This is the 7647th most frequent Russian word.
живущая
"Living" or "existing."
In this sentence, "живущая" is a participle used to describe "Эмили" (Emily), providing additional information about her.
Эмили, живущая в центре города, каждый день гуляет в парке.
Emily, who lives in the city center, walks in the park every day.
Here, "живущая" is functioning as a participle describing the noun "деревня" (the village), indicating its lifestyle and practices.
Деревня, живущая по старинным обычаям, привлекает многих туристов.
The village, living by old traditions, attracts many tourists.
This usage of "живущей" is a participle in the dative or prepositional case, modifying "девушке" (girl) in the context of the book's story.