Well, then why don't you explain it to me, which I am sure you won't because I can never get one of you to step up to the plate.
Sure.
A republic, from the Latin
res publica is a government where the affairs of state are considered a public matter, rather than the private concerns of autocrats, oligarchs, and dictators.
A democracy, from the Hellenic
demos kratos (literally people rule) is a governmental system where the people get to choose who their leadership is.
You should note, right off the bat, neither term contradicts the other, in fact they are complimentary in many ways. Democracy originated in
Athenai where it went through a few changes over time; at times it was a direct democracy in which all matters were voted on by the majority of the population (what we might know as a direct democracy), in other situations decisions were made by assemblies, which could be secured by drawing lots. At its height Athenian Democracy was a complex state of affairs, further complicated that only land owning male Citizens could vote, which were only about 30% of Athens's population.
Athens was not a representative democracy, but Rome was; Senators were elected by votes from Citizens and were supposed to represent them in the Senate and in Assemblies. We know of course that Rome's democracy was highly stratified due to the heavy influence of wealthy landowners and aristocrats, known as Patricians, who held significant sway, but Rome still had a democracy, and when incensed the mob, the Plebeians, could prove a powerful political force.
So what is the United States? Well we are clearly a democratic republic, specifically a Federal Presidential Constitutional Republic Representative Democracy. We are a Federation, Federal, because we composed of 50 self-governing states. We we have a Presidential system, where the head of government leads an executive branch that is separate from the legislative branch. We are a Constitutional Republic, because our Constitution is the supreme law of the land, and we are a republic because the affairs of government are the common sphere of all American citizens. We take part in government through our Representative Democracy, where instead of all 325 million of us voting on all things together, we elect representatives to represent us in the government and act on our behalf.
We are both a democracy and a republic, and those terms do not contradict each other as we have defined them. Now, if we were a direct democracy you could make the argument we were not a Representative Government and by some definitions not a Republic, but that gets into technicalities which do not apply to the United States, or indeed most nations. Switzerland has strong elements of direct democracy, but they are still a republic after all.