The Aztec civilization was primarily composed of three major cities. The capital was called Tenochtitlan and was located in the same place as modern-day Mexico City. The other two cities were called Texcoco and Tlacopan, which were also located in what is now known as Central Mexico.
Many modern-day Mexican people are likely descended from the Aztecs, although it is sadly difficult to trace because of the European colonization. It is important to remember that many elements of the culture we associate with the Aztecs were not limited to those three cities, but were common to the entire Mesoamerican region, which roughly covers modern-day Mexico, Belize, Guatemala, El Salvador, Honduras, Nicaragua, and Costa Rica. So even though the Aztec civilization did not technically extend to those places, you may often see the term linked to their history because of the overarching cultural similarities.