Why did the battle happen?

Answer 1

The Greek cities planned to first destroy the Persian fleet to eliminate its amphibious threat to their individual cities. This would then allow them to concentrate their armies to defeat the Persian army, rather than keeping them defensively at home.

The therefore blocked the pass at Thermopylai with a small fore to compel the Persian navy to attempt to turn the position by sea. The Greek fleet lay in wait at the nearby strait at Artemesion to emgage the Persian fleet.

Unfortunately for the Greeks they lost and withdrew the force blocking the pass as it now had no further purpose.

The Greek fleet then tried again at Salamis and won. Their armies combined the following spring to defeat the Persian army at Plataia.