Democracy is an overused term, as it is applied to revolutions and governments.  We are a republic with democratic institutions.  We elect people to make decisions for us because it would be too cumbersome and inefficient to have everyone participate in direct democracy.  Everyone who is a citizen and 18 can vote.  That's democratic.  Everyone can go to school.  That's democratic.  And the Bill of Rights applies to everyone in the country.

The US government is not a pure democracy. It's a democratic republic. This means that we elect leaders, and representatives, but we also have a check on pure democracy known as the electoral college so that presidents are not direcly elected.

The U.S. is not truly a democracy, we are a federal republic, specifically we are a democratic federal republic because our officials are elected by all the people. The term federal refers to the fact that we are in truth, a union of states with a federal government.  This term may become more important in the near future if any of the states with secession legislation on their dockets actually tries to vote on this legislation. (See bills in New Hamshire, Arizona and several other states)   The term republic comes from ancient Rome rather than Greece and a Republic is a modified type of  Democracy.  True Athenian Democracy does not work in a large state.  It is unmanageable.