This is the 19568th most frequent Korean word.
어두워지기
"Getting dark" or "becoming dark."
In this sentence, '어두워지기' is used to describe the beginning of the action of darkening in relation to the sky.
하늘이 어두워지기 시작했어요.
The sky has started to darken.
Here, '어두워지기' is applied to refer to the inevitable darkening of surroundings after a movie ends.
영화가 끝나면 주위가 어두워지기 마련이에요.
When the movie ends, the surroundings are sure to darken.
The usage of '어두워지기' in this sentence indicates the condition of impending darkness happening shortly.