The government structure of the Aztecs was based on the family unit. Multiple family units owned land collectively, and these groupings were known as calpulli. The capulli was around long before the Aztec empire and included a local governing council who were responsible for maintain schools and collecting taxes.
The capulli that grew into cities like Tenochtitlan became more influential and larger. They in turn elected an executive council which contained a tlacani, or singular leader who would control the city and the surrounding lands.
The leader of the city of Tenochtitlan became known as the Huey Tlatcani, or Great Speaker, also known as the emperor. He was worshipped as a god and supported by the priests and warriors. He could be removed from power since he was technically elected through the tlancani system, but this was rarely done.