The Athenian historian Thucydides, who lived through the Peloponnesian War and wrote the history of it, began by asking, why did the war start? He answered that basically the war started because Athens was too greedy, and tried to take over all of Greece. So the Spartans decided to stop the Athenians, and help all the cities of Greece become free and independent. The Spartans formed an alliance with Corinth and some other, smaller Greek cities, and brought an army to march to the walls of Athens in 431 BC.
In the first years of the war, it must have seemed pretty hopeless. The Athenians had a lot of money, and a lot of power, and they were the only Greek city that had a good navy. Even though the Spartans could attack the countryside around Athens, the Athenians were safe inside their walls, and the Spartans could not break through. And the Athenians could get food, and come and go as they pleased, by sailing out of their port in their ships. The Spartans didn't have any navy, so they couldn't stop the Athenians from sailing around.
But in the summer of 430 BC the Athenians began to die from a terrible plague. Because all the Athenian farmers had to leave the countryside and move inside the walls of Athens, it was very crowded inside the walls. A lot of poor people were living in wooden shacks, a lot of people in one room, and with no real protection from the weather, and not enough good food to eat. So it was easy for the plague to spread.
We don't know exactly what this plague was. Even though Thucydides described it, it doesn't sound exactly like any modern disease. Some people think it might be a stronger form of measles. But hundreds of people died. One of them was the Athenian general Pericles, who had been leading the war.
Gradually the Spartans began to win some battles.