Why was Sparta one of the most powerful cities in Ancient Greece?

Sparta was famous for its army. Boys from an early age were raised in harsh conditions, making them skilled and fearless warriors. Love for the homeland, Sparta, was instilled. The need to keep the conquered peoples (helots) in obedience forced the Spartans to hone their military skills and always be ready for war.

The Spartans, unlike the Greeks, did not respect luxury, they tried to live as simple as possible. This, no doubt, further tempered them.

Thus, the army of Sparta was perhaps the most powerful in all of Greece.