This is the 924th most frequent Russian word.
общественных
"Public" or "social."
Here, 'общественных' modifies 'наук' (sciences), referring to the academic field that deals with society and its structures.
Время нужно проводить в изучении общественных наук.
Time should be spent studying social sciences.
In this context, 'общественных' describes 'мероприятиях' (events), meaning events that are oriented towards or for the public.
Они часто участвуют в общественных мероприятиях.
They often participate in public events.
In this sentence, 'общественных' describes 'организациях' (organizations), implying organizations that serve or concern the general public.