Paul W. answered 12/02/19
Dedicated to Achieving Student Success in History, Government, Culture
Different scholars have different opinions about what features an urban settlement requires in order to qualify as an actual 'city'. Keep in mind that the very notion of a 'city' is an artificial construct, a concept invented by human beings, rather than, say, a geographical feature that exists independently of human beings.
That being said, the features of an urban settlement that are absolutely necessary for one to qualify as a city include:
1.)-Density - The number of people living in a designated, limited space. In short, cities have relatively large populations in a relatively small space. Houses and other buildings are crowded together, arranged along some form of streets (these are not necessarily paved or dirt roads, they can also be canals along which to move by water transport).
2.)-Permanence - A city may rise and fall, it may ultimately be abandoned. But a city exists as a permanent form of settlement. It may not have started as an intentionally permanent urban settlement, but with the passage of years, if the settlement remains in one location for an extended period of time and if there is no intention of relocating the settlement periodically, then it is a city. Exactly how long an extended period of time needs to be in order to qualify as a city is difficult to say, but certainly more than a single year and usually many decades, if not many centuries.
3.)-Government - An urban settlement must have some form of municipal government that performs certain basic functions, such as maintaining a degree of law and order, organizing the defense of the city in time of war, etc... Municipal government can come in many different forms: theocratic (combining religious and secular functions), autocratic (a government that does not seek consensus from those who are governed, but imposes its will regardless of the feelings of the city's inhabitants), democratic (government officials who are elected by some or most of the city's inhabitants), etc... Whatever form it takes, a city's municipal government has to be at least to some degree effective, respected and / or feared by most of the city's inhabitants.
4.)-Non Agricultural Economic Activity - Many or even most of the inhabitants of a city may make their living as farmers growing crops and raising domesticated animals. But a city must contain a significant number of inhabitants who make their living through occupations that do not involve agriculture, particularly the manufacture and selling of a variety of goods. This is what makes cities centers of trade, attracting merchants and private individuals who are seeking goods from abroad, from outside of the city, who bring goods for trade to the city and purchase other goods for trade from merchants and craftspeople living in the city.
The urban settlements of the Aztecs, Mayans, and Incas, among other Pre-Colombian civilizations, certainly had all of these four features - their urban settlements were indeed true 'cities', as much as urban settlements in Medieval and Early-Modern Europe, Africa, the Middle East, and Asia. Urban settlements such as Tenochtitlan, Chichen Itza, and Cuzco, to name but three examples. All three had high population densities - that is, large populations in the thousands and tens of thousands. All three existed as intentionally permanent settlements - even if Chichen Itza was eventually abandoned. All three had forms of functioning governments that imposed forms of law and order on the inhabitants of these cities. All three were centers of non-agricultural economic activity, with craftspeople manufacturing and selling goods, with merchants purchasing and selling goods, and with people who lived outside of the cities traveling to the cities to buy and / or sell goods.