To repel a Persian attempt to incorporate the ones in central and southern mainland Greece into their empire.
The Persians gave up after several defeats over thirty years.
The Greek cities which had united under Athens' leadership for the latter part of the 50-years of war then found themselves trapped in the league, with Athens turning it into an empire of its own.
Persian
Against the Persian invasion.
Self defence.
Pony express
Sink or swim - either stop the incessant warfare between each other and unite against the Persians ally and fight, or surrender. Some city-states fought in alliance, some joined the Persian side.
Exercising his power of king through his generals.
It was in their interests to join with the other Greek city-states in a coalition to defend their mutual interests and cities.
He provided them a share in the spoils of conquest of the Persian Empire using Greek city soldiers, while using his influence in the Amphictyonic League to keep the Greek cities quiet.
To marry his generals to Persian aristocracy an produce a hybrid ruling class. To introduce Greek-style cities to spread Greek culture. To introduce Greek as the lingua franca.
Some joined the Persians with their armies. A third of the Persian fleet was from Greek cities in Asia Minor. The southern cities united their fleets to fight at Artemesion. They then fought together at Salamis, and the following year at Plataia and Mycale. Then Athens led the Delian league for the next thirty years until a peace was made with Persia.
They united 180 Greek city-states into several alliances, the first led by Sparta, the next led by Athens.
First they bribed the aristocracies of the northern Greek cities to join them. Then they used their fleet to threaten the southern Greek cities which kept their armies at home to protect themselves against amphibious invasion. They then planned to defeat the Greek fleet to ensure the cities continued to keep their armies at home and not unite, so the Persian army could pick the cities off one at a time. The Greek plan was to destroy the Persian fleet o remove the amphibious threat and collapse the Persian sea resupply system. As their fleet destroyed the Persian one at Salamis, the Persian plan went astray, and with no amphibious threat, the Greek cities were able to send out their armies to unite and defeat the Persian army (of which half was sent home as they could not be resupplied) at Plataea. Two good strategies, the Greek one triumphed because of the sea victory at Salamis. If the Persians had won there, the result would have been reversed.