For starters, no Thermopylae did not change the world, the Greeks did not win, freedom and democracy were not preserved, and the Persian invasion was not significantly halted. In truth, Athens still burned and the Spartans did not die alone.
Now that these popular myths are out of the way, how important was Thermopylae?
Militarily, Thermopylae was a well-planned battle that maximized the advantages of holding narrow terrain. A narrow pass meant that Xerxes could not deploy his entire army around the Greek phalanx. Thermopylae’s location also helped force the naval battle at Artemisium, which for obvious reasons, threaten the resupply and longevity of Xerxes army in the field if successful.
In short, Thermopylae did make sense as a holding action if the intent was to win the navy battle at Artemisium. As a delaying action, general engagement, or even a last stand (as popular histories go) not so much. In fact, given the performance of the Phocians at guarding the pass around Thermopylae, the battle could even be described as a blunder. No one should have been surprised -least of all Leonidas- that the Persians would try to find a way around Thermopylae after having failed with frontal assaults. Not appointing quality sentries to guard such a critical juncture then is hard to excuse.
Having said that, Thermopylae arguably did provide some shock value. The greatest land army ever seen -in the presence of Xerxes himself- was stopped for three days. However, its not clear exactly -as its been argued intelligently on these forums before- how many Persians died at Thermopylae (only Herodotus says 20,000). No matter the blow to Persian morale (or loss of troops), it was not enough to dent the Persian advance, and probably still not as significant as the death of a spartan king or the sack of Athens.
In short conclusion, I’d argue Thermopylae was mostly insignificant. The entire war was still left to be determined. And more than decisiveness, the battle of Thermopylae should be defined more by mistakes and opportunities lost then any kind of earth-shattering turning point for either side.
Go tell the Spartans, oh stranger passing by, that Thermopylae, more or less, was something just to pass by.