Answer:
Calpulli, which means roughly "big house" in Nahua, the language spoken by the Aztecs, was the fundamental core of Aztec society, an organizational unit broadly corresponding to a city ward or a Spanish “barrio.” More than a neighborhood, though, the calpulli was a politically-organized, territory-holding group of peasants, who lived near one another in rural villages or in neighborhoods in larger cities.
The Calpulli's Place in Aztec Society
In the Aztec empire, calpulli represented the lowest and most populous social unit under the level of the city-state, called in Nahua an altepetl. The social structure looked mostly like this:
The top level consisted of the member cities of the Triple Alliance: Tlacopan, Tenochtitlan, and Texcoco. The highest administrative authorities in the Triple Alliance were called Huetlatoani.
Subject to the Triple Alliance were the altepetl (city-states), led by a dynastic ruler known as a tlatoani (plural tlatoque). These were smaller urbanized centers which had been conquered by the Triple Alliance.
Finally, calpulli were small rural villages or wards in altepetls or cities, led by chiefs and a council of elders.
In Aztec society, the altepetl were connected and aligned city-states, all of whom were subject to the authorities at whichever city had conquered them, Tlacopan, Tenochtitlan, or Texcoco. The populations of both big and small cities were organized into calpulli. At Tenochtitlan, for example, there were eight distinct and roughly equivalent calpulli within each of the four quarters that made up the city. Each altepetl was also made up of several calpulli, who would as a group contribute separately and more or less equally to the common tax and service obligations of the altepetl.
Organizing Principles
In the cities, the members of a particular calpulli typically lived within a cluster of houses (calli) located near one another, forming wards or districts. Thus "calpulli" refers to both a group of people and the neighborhood they lived in. In the rural parts of the Aztec empire, calpulli often lived in their own separate villages.
Calpulli were more or less extended ethnic or kin groups, with a common thread that united them, although that thread varied in meaning. Some calpulli were kin-based, related family groups; others were made up of unrelated members of the same ethnic group, perhaps a migrant community. Others functioned as guilds—groups of artisans who worked gold, or kept birds for feathers or made pottery, textiles, or stone tools. And of course, many had multiple threads uniting them.
Shared Resources
People within a calpulli were peasant commoners, but they shared communal farmlands or chinampas. They worked the land or fished, or hired non-connected commoners called macehualtin to work the lands and fish for them. The calpulli paid tribute and taxes to the leader of the altepetl who in turn paid tribute and taxes to the Empire.
Calpullis also had their own military schools (telpochcalli) where young men were educated: When they were mustered for war, the men from a calpulli went into battle as a unit. Calpullis had their own patron deity and a ceremonial district with administrative buildings and a temple where they worshiped. Some had a small market where goods were traded.
The Power of the Calpulli
While the calpulli were the lowest class of the organized groups, they were not poor or without influence in the greater Aztec society. Some of the calpulli controlled lands up to a few acres in area; some had access to a few elite goods, while others did not. Some artisans might be employed by a ruler or affluent noble and compensated handsomely.
Commoners could be instrumental in a significant provincial power struggle. For example, a populist uprising based in a calpulli in Coatlan was successful in calling in the Triple Alliance to help them overthrow an unpopular ruler. Calpulli-based military garrisons were dangerous if their loyalty wasn't rewarded, and military leaders paid them handsomely to avert massive looting of conquered cities.
Calpulli members also played roles in society-wide ceremonies for their patron deities. For example, calpulli that were organized for sculptors, painters, weavers, and embroiderers played significant active roles at ceremonies dedicated to the goddess Xochiqetzal. Many of these ceremonies were public affairs, and the calpulli participated actively in those rituals.