"A Justification for Minority Rule"

"You can have democratic republics like the United States, where the elected president is both head of government and head of state. You can have democratic monarchies, like the United Kingdom, where the elected prime minister is the head of government while the monarch is head of state. You can have authoritarian republics, like Russia, and authoritarian monarchies, like Saudi Arabia.                                                    "Lee's definition of 'democracy' is out of step with both the way the founders used the term and the way most political observers use it today. It is an idiosyncratic definition found almost exclusively among American conservatives—in a way that reveals some deeper problems in the modern conservative project." 

Zack Beauchamp at Vox explains the meaning behind saying that the United States is a "republic not a democracy."