The Greeks contributed to democracy primarily through being the foundation of Western Civilization democracy. It all started in Greece and mainly in the city of Athens. Cleisthenes, who was a statesman, is considered as the founder of democracy in Athens. Cleisthenes introduced insightful reforms. These reforms caused democracy to exist as a system of government for the first time worldwide. In fact, the word “democracy” comes from two Greek words. These are demos = people, and kratein = to rule.

Democracy in Athens consisted of the Assembly (ekklesia); the Council of Five Hundred (boule), and the Popular Courts (dikasteria). As noted in the above answer, Greece’s democratic experiment eventually spread to other city-states in the country as well as into parts of Europe.

Cleisthenes introduced his form of democracy to Greece in 507 B.C. The heart of democracy in Athens was to enable all citizens over the age of 20 to have a hand in the governing of the nation.

A focus of the thinking pertaining to democracy in Greece was what Herodotus, a Greek historian, said, “In a democracy there is, first, that most splendid of virtues, equality before the law.”

Source: Ancient Greek Democracy: Demokratia and the Demos

It came to be that most democracies selected a group of men who would do the most vital voting. This was because it was difficult for ordinary systems to always get away to meetings as they worked in agriculture or the trades or were soldiers and couldn’t always be expected to attend democratic meetings to decide and vote on issues. However, when it came to very weighty votes, these men typically attended. In Athens, this was accomplished through the above-mentioned Council of Five Hundred.

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The Greeks, and particularly the Athenians, were one of the first peoples to form democracies.  Thus, their contribution to democracy is that they helped to pioneer democracy and then passed it down to the Romans and, eventually, to European countries.

By the time of Pericles (mid to late 400s BC), Athens had become quite democratic.  All male citizens over the age of 18 were given a voice in the government of the polis.  The people had a great deal of control over those who were elected to govern them.  This was a fairly strongly democratic system.

The Greek democracy helped to influence the Roman republic.  Both of these types of government eventually influenced thinkers in Europe who pushed their own countries (and offshoots such as the United States) towards democracy.