I believe that what you are asking about is the role that the Teotihuacan played in "creating" the Aztec people.
The Aztecs came to the Valley of Mexico as essentially a bunch of barbarians from the North. When they got to the Valley, they found the ancient city that was, by this time, deserted. They used the city's culture to create one of their own. For example, they borrowed many of the aspects of Teotihuacan's religion.
By using the religion and to some extent the culture of the ancient city, they gave themselves legitimacy. Instead of a bunch of barbarians, they were the heirs of the culture of Teotihuacan.