This is the 1052nd most frequent Russian word.
общий
General; common; shared.
Here, 'общий' is used as an adjective meaning 'general', describing the plan as one that applies to all or overall.
Мы обсуждаем общий план развития.
We are discussing the general development plan.
In this sentence, 'общий' means 'common', referring to something shared between multiple parties, specifically the interest.
У них есть общий интерес в этом проекте.
They have a common interest in this project.
Here, 'общий' denotes 'common', suggesting the hall is for shared use by a group of people.