Assemblies, generally, are gatherings of men and women in a community.
The reference to peaceful assembling we recognize from The First Amendment to The Constitution for The united States of America, has been with the intent of expressing the will of a people, most often for presentment to those in some governing capacity.
American history refined this understanding of peaceful assembly rather quickly into those groups of men whose discussions and subsequent efforts were to improve the lot in life for themselves and their neighbors by redressing grievances held due to misrepresentation by governing agents, e.g., the king and his representatives.
Modern reference to exercising our God given right to freely assemble is typically with specific, articulated purpose: acting as jurists in the context of a Grand Jury to ensure that the express will of the people, and their redress of grievances, be fairly and equitably applied: Justice.
Below are links to a few of the historical supports for this type of purposeful civic gathering.