The Hellenistic cities were meant as sources of economic, military, and political power for the Greeks who were ruling the Hellenistic empires. While they had this impact, they also had the impact of spreading Greek culture across much of Asia, as far as what is now India and Afghanistan.
The cities served as outposts for the military and as major centers of commerce. In addition, they were politically helpful because the Greeks and the local rulers who controlled the cities needed one another. This allowed the Greeks to control the cities and, thereby, the areas around the cities.
In addition to these practical roles and impacts, the cities served as places that spread Greek culture. In the cities, arts, architecture, religion, and other cultural things were all Greek. This had the impact of spreading the culture far beyond the Greek homeland.