To be exact: democracy and the things that came with democracy. Do not confuse Greek democracy with today's democratic ideals. For instance, women did not have any rights in Greek democracy and of men, only a small number of elite had a say so. However, even this could be considered perfect for that time.
What did democracy bring: at first it gave enough ground to the Greeks to colonize the rest of the old world. By ground, I mean a political will and power. This in turn, brought prosperity to the Aegean. The accumulation of knowledge did not happen mostly in today's Greece, but instead western Turkey. In this part, the eastern Aegean, we can see smaller autonomous regions, where the leaders put the money into use, not only by building ships and hiring mercenaries, but also by hiring engineers, mathematicians and artists. This in turn, increased the rate of accumulation of the common knowledge. Just to give you an idea, money was invented, knowledge of geometry spread, theater was a part of daily life. Libraries, amphitheaters, temples of knowledge were all products of this time. And last, but foremost was philosophy. Sophists were the first teachers and naturalists were the founders of all positive sciences. And Greek civilization formed the basis for Romans. So that is why we regard Greek civilization as the cradle of western civilization. I hope it helped you a bit because "all I know is that I know nothing".
emocrazy