Athens at the dawn of the 6th Century B.C. was an unremarkable city. The arts, science, and philosophy that would make it great were still centuries away.
The only notable thing about Athens of the time was its relatively large size, which was also the source of its problems. Athens was too large to feed itself and this was becoming a crisis.
Athens was ruled much like other Greek cities after the collapse of the Bronze Age, by an oligarchy.
On the political side, the vying of aristocratic families was tearing the city-state apart. The city of Athens was run by nine archons. These archons were elected for one-year terms by a council of former archons called the Areopagus. Archonships were available only to members of the aristocracy. These aristocrats used their position and power to benefit only their own family. The only political body capable of calling these people to task was the Areopagus. Since the only check on aristocratic power was other aristocrats, the needs of the rest of the population went unnoticed.Athens was slightly ahead of the curve in that it had an existing Constitution, but that Constitution merely enshrined the power of the oligarchy.
The aristocratic families were bitter rivals and battled over whatever scraps of wealth the society produced. This system was so inefficient that even they had to conceed the need for a third party to institute reforms. So every ten years they selected a tyrant. Some were worse than others. In 621 BC Draco, the namesake of the word "draconian", codified a set of "notoriously harsh" laws that were "a clear expression of the power of the aristocracy over everybody else." The punishment for breaking Draco's laws was almost always death. This did not stop the aristocrats from feuding.
Enter an ancestor of Plato, Solon, the lawgiver.
Solon who also came from an aristocratic family, made a name for himself by winning a minor war against a nearby Greek tribe.
When the Areopagus selected Solon in 594 B.C. they almost certainly did not expect sweeping reforms that would forever change Athens, but that's what they got.