The geography of Ancient Greece had much to do with the rise of the Greek City-State or Polis. The difficulty in travel from one Greek City State to another kept government in the hands of the City States even though they may have been ruled by some other country. In Athens, a form of government known as Democray came to be. Pericles did much to advance rule of the people for the people. In Athens, all citizens had their name in the a lottery of sorts to serve in the Assembly. It made it equally attainable to all Greek Citizens without regard to their economic or social standing.
The type of Democray practiced in Ancient Greece is called pure Democracy. This literal means that all the people participate in the making of laws because each of them had an equal chance to be part of the Assembly.
So what do we practice in the United States? Textbooks tells us we practice Representative Democracy--that is people in a region vote for someone to represent their interests in Congress.