The Persian war started with tensions between Athens and Sparta in the 6th century BC. Sparta had opposed the Athenian democratic reformer Cliesthenes, and intervened politically on behalf of the Athenian aristocracy. Athens was upset by this and sent representatives to Persia to ask for an alliance to protect against any more Spartan incursions.
The Persians viewed themselves as the greatest nation in the world. Because of this, they did not make bilateral agreements with anyone. In order to seal the agreement, Persia demanded tokens of Athenian earth and water. The Athenian representatives thought that the Persians just wanted superficial gifts. But, according to Persian diplomatic protocol, tokens of earth and water meant that Persia had sovereignty over the other country’s land and sea. The Athenians were upset when they discovered that they had entered into an agreement as inferiors, but they never actually ended the agreement. This misunderstanding set the stage for the Persian wars.
Hostilities started when Athens sent 20 ships (a substantial force for Athens at the time) to assist an Ionian Greek uprising against the Persians in 499 BC. The Persians were very upset with this and sent legates demanding tokens of earth and water from all the Greek city-states. When they came to Sparta, they were murdered. Persia sent ships to Greece as a show of force, and started the war.
The Greeks defeated the initial Persian invasion at the battle of Marathon. After eleven years and a second Persian invasion, Greece, and namely Athens and Sparta, emerged victorious. This was an amazing victory for the Greeks. Persia was a huge empire and Athens was so tiny that the Persian Emperor didn’t know it existed until the failed agreement between them.
After the war the Athenians got together with several other city-states, and formed the Delian league, just like the Spartans and their Peloponnesian league. This league was meant to protect Greece in the event of another Persian invasion, but eventually was used to make Athens richer and more powerful. This set the stage for the devastating Peloponnesian war between the Delian league and the Peloponesian league, which weakened all of Greece and changed the course of western civilization.