This is the 5789th most frequent Russian word.
прошедшей
"Of the past" or "past" (feminine form, genitive case).
Here, 'прошедшей' (past) modifies 'неделе' (week), denoting the concluded week that recently passed.
На прошедшей неделе мы ходили в кино.
Last week, we went to the cinema.
In this sentence, 'прошедшей' describes 'конференции' (conference), referring to the event that has already occurred.
В прошедшей конференции участвовали многие учёные.
At the past conference, many scientists participated.
The word 'прошедшей' characterizes 'встрече' (meeting), indicating the meeting that has taken place in the past.