This is the 15977th most frequent Russian word.
прошедшая
"Прошедшая" means "past" or "elapsed" (feminine form).
The word "прошедшая" is used as an adjective describing "week" to indicate it happened in the past tense.
Прошедшая неделя была очень продуктивной.
The past week was very productive.
Here, "прошедших" is inflected for plural and is modifying "events" to denote they occurred earlier.
Он рассказал о прошедших событиях.
He talked about past events.
In this sentence, "прошедшее" functions as a noun meaning "the past time," abstractly referring to time that has elapsed.