How were the Spartans able to hold off such a large Persian army in the battle of Thermopylae

The Spartans, alongside other Greeks were able to hold the Persians by fighting in the narrow pass of Thermopylae with the sea on one side and cliffs on the other. They were able to withstand the Persian assault for three days as the Pass was only wide enough to allow a few men to face each other at once, as well as the heavier Greek armour and better weapons, and Persia’s lack of familiarity fighting infantry in a Phalanx. At sea the Athenian general Themistocles fought the battle of Artemisium and kept Persian’s from outflanking the Spartans by sea.

Another View:

The purpose of holding the pass was to force a sea battle to defeat the Persian fleet ans so remove the threat to the southern Greek cities which kept their armies at home to defend against an amphibious attack (including Sparta – the Spartan contribution at Thermopylai was Leonidas’ personal bodyguard). If the Persian fleet could be destroyed this threat would disappear, and the Greek city-state armies could come out to battle the Persian army.

So the central Greek cities sent contingents to help hold the pass – about 5,000 warriors. When the sea battle failed, there was no point in holding the pass, and Leonidas sent the contingents off to seek protection in friendly city walls. He held the pass with his Spartan 300 heavy infantry and their 2,000 light infantry to allow them to get away before the Persian cavalry broke through and rode them down in open country.

A noble sacrifice for others, not the mindless fight to the death which is so often presented as.