A pure democracy is where every person gets a say in how every part of the government is run.  Like for instance everyone would come together in a town to vote and decide on what would be best for everybody.  It's quite idealistic and can be prone to abuse in this way:\n\nIn a democracy, the ones who are largest and loudest have the most power.  Therefore a whole people could be wiped out if the majority said "everyone with brown hair must die."  Also as times goes on, the democracy deteriorates into a dictatorship as the most power pursuing persons gain more and more power over the others.  A classic example is the deterioration from Lenin's Communism to Stalin's dictatorship later on.  It's the closest thing to a pure democracy that has existed as of late.\n\nAs for a Democratic Republic well that's what we have.  It's democratic because we vote for whose in office.  It's a Republic because it has the legislative, judicial, and executive branch.