This is the 2093rd most frequent Russian word.
общая
General; common; shared.
Here, 'общая' is used as an adjective describing the noun 'цель' (goal), indicating that this goal is shared among multiple people.
У нас есть общая цель.
We have a common goal.
In this context, 'общая' again functions as an adjective, describing 'комната' (room) as being used collectively or owned jointly by a group.
Это наша общая комната.
This is our shared room.
Here, 'общая' modifies 'осведомленность' (awareness), implying a broad or general understanding.