The battle of Salamis occurred in September 480 BC, some argue it was on the 22nd others say the 29th, we are unlikely to ever be certain.
This was one of the most important engagements between the Persians and the Greeks during the Persian wars and occurred immediately after the defeat of the Spartans (and their allies) at famous battle of Thermopylae.
The victory at Salamis was vitally important to the Greek war effort against the Persians because, in essence, it denied the Persian forces naval superiority which dramatically reduced their options regarding the conduct of the remainder of the invasion of Greece.
The Persian king Xerxes was invading Greece because the mainland Greeks (particularly the Athenians) had participated in the Ionian Greek rebellion against the Persian Empire.
They had already made a tentative strike some years earlier at the battle of Marathon where they were defeated by the Athenians. Xerxes had decided on a full scale invasion of Greece with a massive force of men and ships. Herodotos, the main source for the events of the invasion, provides what are generally agreed to be fanciful numbers of the Persian forces suggesting that a million Persians and more than 1200 ships were involved in the invasion. Even if Herodotos’ numbers are significantly reduced it should be noted that the Greeks were likely to have been heavily outnumbered by the Persian forces.
The battle itself occurred in the narrows between the island of Salamis and mainland Greece, much like the battle of Thermopylae presented a confined space that favoured smaller forces.
The Greek forces were already in the narrow straits, the Persian forces were arrayed at the south end of the straits in the open waters. Themistocles, the general of the Greek forces, was faced with a significant problem, the allies debated the best way forward in the defence of Greece. Themistocles, unwilling to present northern Greece to the Persians and defending at the Isthmus of Corinth, organised for the Persian forces to receive word that the Greek fleet was ready to flee. Xerxes also wanting to bring the war to a head sent his ships forward into the straits and sent a contingent of Egyptians to the north end of the straits to block any attempts at escape.
Greek understanding of the terrain again came to the fore, the massive Persian fleet moved into the straits but were hindered by their numbers getting in each other’s way and creating a disorganised mess. The numerically smaller Greek forces were able to take advantage of the confusion and disarray. The details of the battle are at best vague the Persians were expert sailors with high quality ships (contrary to many commentaries) however like at Thermopylae their marines were far more lightly equipped than the Greek marines. As the ships came together rams sank some vessels sheared the oars off others and others still were boarded with marines fighting for control.
The Persian navy was routed, with the ships further fouling each other in their retreat towards Phaelerum. The Greeks won a major victory, as many as half of the Persian ships were destroyed, the Persian forces abandoned Attica, Xerxes with the larger part of his army left Greece and returned to Persia. The Few forces remaining in Greece stayed under the command of Mardonius, who was later defeated by the Greeks at Plataea and Mycale ending the invasion of Greece.