This is the 2457th most frequent Korean word.
다가오는
"Approaching" or "upcoming."
In this sentence, '다가오는' modifies '주말' (weekend) to denote the weekend that is approaching.
다가오는 주말에 가족과 소풍을 갈 계획이에요.
We are planning to go on a picnic with the family during the upcoming weekend.
Here, '다가오는' describes '시험' (exam), referring to the exam that is soon to occur.
그녀는 다가오는 시험에 대해 걱정하고 있어요.
She is worried about the upcoming exam.
In this example, '다가오는' applies to '계절' (season) to indicate the season that is arriving.