What was the purpose of an acropolis in Greek city-states?

The acropolis was a place of gathering where one was able to congregate with others and often was a place to worship that city-states god or goddesses such as the Athenian Parthenon that worshiped Athena, but the acropolis also served as a place that could protect citizens from attacks due to its elevation

Where the people could retreat to if under attack.

Explanation:

Acropolis means 'high city' in Greek. Most city-states in ancient Greece had at their centre a rocky mound or hill where they built their important temples and where the people could retreat to if under attack.