Why did the Greeks defeat Xerxes?

Xerxes was disturbed by the interference of the Greek city-states of mainland Greece who supported revolts by Greek cities within his empire.

He bribed some cities in Central Greece ti fall into line, but the Southern city-stated refused, so he set out to subdue them and install friendly governments in them, and install a Persian governor to supervise them.

This invasion was at first successful, getting as far as Athens, but his fleet was defeated by a combined Greek fleet at Salamis in 480 BCE. Elimination of the Persian fleet, which was the first strategy of the Greek alliance, took away the Persian amphibious threat to the Greek cities which had kept their armies at home to defend against this. The Persians were able to pick the cities off one by one.

So the cities were now abled to send their armies out to join up and defeat the Persian army the following spring at Plataia, while their fleet finished off the Persian fleet at Mycale in Asia Minor where the remnant was holed up.

Another effect of the naval victory at Salamis had been that the Persian fleet could no longer protect the Persian supply fleet which sustained the army, and half the Persian army had to go home, which gave the Greek army an edge against the reduced Persian army and it's Greek allies at the deciding battle at Plataia in 479 BCE.

With the Persian main forces defeated, the invasion was over, and the war moved on to isolated engagements in the eastern Mediterranean over the next 30 years, until the Persians gave up and left the Greeks to go back to their usual fighting amongst each other.