Because if the Spartans did not hold them off ( temporarily ), the Persians would have marched right on into Greece and would have defeated them entirely. Thus ending Democracy as we know it today. The time that was bought by the Spartans was used for the rest of Sparta and other Greek City States, namely Athens (Navy) to get their acts together and prepare for and all out battle or death. We'd probably be foreign slaves right now, or better yet, North America may still not even be found for all we know.
Anyway in the time of the battle of Thermopylae (480 BC), the Greeks did indeed get their acts together and the combined ships of the Navy's handed the Persian navy a crushing defeat in The Battle of Salamis. The last battle of the war was back on land, The Battle of Plataea. This time the Spartans had their army ready to battle along with Athens, Corinth, Magara and many, many other Greek City States. Persia was beaten badly and thus ending their attempt to enslave all of Greece. This brought on the forming of The Delian League in 478 BC where around 150 Greek City States united together to stop future Persian attacks.
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It saved the citizens of Athens from having their ex-tyrant Hippias, who they had expelled, restored by the Persians, who wanted to use him to stop Athens from interfering in support of the rebellious Greek cities within their empire.
As part of a Greek blocking force, they helped hold the pass for three days to make the Persians try to break through by turning the bottleneck by sea. The Greek navies were waiting offshore to pounce on the Persian navy to try to eliminate it and its threat to the Greek cities. As it turned out, the Greek navies were defeated and withdrew to try again at Salamis. The land blocking force at Thermopylae, its mission now invalidated, withdrew. The Spartan contingent of 300 heavy infantry and 2,100 light infantry, together with the Thespian contingent, remained holding the pass to allow the other city contingents to escape to the walls of friendly cities before the Persian cavalry broke through and rode them down in open countryside. They were killed to a man, a noble sacrifice to save their comrades.
PrometheusTheseus
No he does not, she dies.
Cleopatra VII did not save her country. Read a history book! She lost her country to the Roman empire.