What Is a Popular Assembly?
A popular assembly is a self-organized, autonomous, non-hierarchical group of people who come together to meet.
In many cases the assemblies are based geographically (by neighborhood, town, county, state, etc.).
The assemblies are inclusive and develop in process rather than being pre-planned.
Popular assemblies form as a furious alternative to electoral politics. In this era we see everywhere, including the United States , the ownership of elected officials by the large, usually transnational corporations.
It takes direct democracy to the participants and abandons the useless representative government – with good reason; “elected” or assumed (royal or dictatorial) governorship cannot respond to the needs of the ordinary people while simultaneously obeying the financial demands of the World Bank, the International Monetary Fund, and the corporations controlling social agendas, including health, educational and environmental agendas.
By definition, a people’s assembly (asamblea popular) must be anti-capitalist and anti-neoliberal. The hierarchical structure of governments and corporations implies a boss and/or owner who benefits from the work of the people, hires and fires at will, and frequently owns or appropriates the national resources.
The assembly is composed of people who are being screwed and know it.
La Asamblea is not a political party and refuses ownership of political power apart from the social power which comes from below.
It is the counter to individualism; it is community of purpose and goal.
The force that holds it together must be a common goal and vision, not a particular cause.
Taken from: Popular Assemblies and the Growing Popular Assembly Movement commentary from Oaxaca by Nancy Davies
Popular Assemblies in Oaxaca
In the light of this situation, and in the recognition that the state government was repressive and had become effectively powerless in governing, the APPO was created and convened for the first time on June 17, 2006. It declared itself the de facto governing body of Oaxaca . Its body included representatives of Oaxaca ’s state regions and municipalities, unions, non-governmental organizations, social organizations, and cooperatives, the largest group being Section 22, the Oaxacan teachers' union. It encouraged all Oaxacans to organize popular assemblies at every level: neighborhoods, street blocks, unions, and towns. The APPO took the slogan that it was a "movement of the bases, not of leaders" and asserted the need for common civilians to organize and work beyond the scope of elected officials. While the primary demand of the APPO has been the removal of the governor of Oaxaca , they have also called for broader economic, social and political transformations, as well as changes in the state's political constitution. This goal was furthered through the formation of the State Council of the Popular Assembly of the Peoples of Oaxaca (CEAPPO) during the APPO's November Constitutional Congress. The State Council is an effort to create an organization that will outlive the current mobilization and extend beyond the capital city throughout the state. The Council is formed of 260 representatives from the various regions and sectors of Oaxaca , including 40 members of the teachers' union. 
Included in the resolutions of the APPO are a recognition of indigeous rights and autonomy, gender equality, political accountability, opposition to neoliberalism and Plan Puebla Panamá, a demand for an alternative education, and collectively-run media, amongst others.
The Popular Assembly of Oaxaca takes as inspiration indigenous political practices called 'usos y costumbres' (traditional usages and customs) that have been incorporated into the municipal level government of Oaxaca . These practices stand apart from standard electoral politics in that the assembly structure does not include secret voting procedures, but rather open meetings to make decisions.
"'The executive branch' (the authorities) is charged with accomplishing the tasks the assembly gives it. The municipal president, foremost among the authorities, leads (as the Zapatistas’ phrase explains) by obeying. For the population of Oaxaca , the idea of governing by consensus remains part of the common cultural heritage. Therefore, as APPO was convoked, the modest people who comprise 80% of Oaxaca ’s population, recognized it immediately. And they support it, despite the obvious difficulties of convening authorities from around the state. Since these authorities receive no pay, a trip to the capital city is not easy. But it’s happening." 
The APPO has met with officials of the federal government periodically throughout the conflict, but has yet to be able to negotiate a resolution to conflict. Members are currently engaged in efforts to free, and call attention to, APPO leaders detained as suspects of commiting crimes, such as destruction of public property.
Taken from Wikipedia.org (Asamblea Popular de los Pueblos de Oaxaca)