It would have been more accurate to write that the ancient Greeks birthed an ancient form of democracy. For during the course of time the concept of democracy has changed considerably, depending on which country believes it’s self to be a democratic country.
The term originates from the Greek δημοκρατία (dēmokratía) "rule of the people", which was found from δῆμος (dêmos) "people" and κράτος (krátos) "power" or "rule" in the 5th century BC to denote the political systems then existing in Greek city-states, notably Athens; the term is an antonym to ἀριστοκρατία (aristokratía) "rule of an elite". While theoretically these definitions are in opposition, in practice the distinction has been blurred historically. The political system of Classical Athens, for example, granted democratic citizenship to an elite class of free men and excluded slaves and women from political participation.
In virtually all democratic governments throughout ancient and modern history, democratic citizenship consisted of an elite class until full enfranchisement was won for all adult citizens in most modern democracies through the suffrage movements of the 19th and 20th centuries.
The citizens choose and replace the government through free and fair elections;
There is active participation of the citizens in politics and civic life;
There is protection of the human rights of all citizens.
There is rule of law, in which the laws and procedures apply equally to all citizens.
Eligible citizens are able to: 1) vote for the passing/rejecting of laws or run for office during elections, 2) join political parties, sit on boards or committees, and criticise or protest, 3) feel that some of their rights are protected, and 4) receive a fair trial if accused of breaking the country's laws. Politicians represent their constituents in the proposal, development and establishment of the laws by which their society is run.
It remains to be seen whether Tsipras will be able to carry out his election promises!