According to the Oxford Dictionary, the modern concept of a republic is a state in which the people and their elected representatives hold supreme power, and which has an elected president, or a president or prime minister nominated by an elected parliament, rather than an active monarch.
The concept of representative democracy (discussed a few days ago) and the concept of a republic are virtually identical. The U.S.A can accurately be portrayed as a republic, a republican democracy, or a representative democracy.
Excerpted from America: Democracy or Republic?
 From https://en.oxforddictionaries.com/definition/republic. See also: https://www.merriam-webster.com/dictionary/republic.
What I have been wondering is, why does it seem so important to some people to say we are a Republic, not a Democracy?
Hi Juanita, CFFAD does not know why some people (and many bots) make that claim. Regardless of why some make that claim, the truth is our governments are both (representative) democracies and republics. See our short course America: Republic or Democracy. Click here: https://cffad.org/america-republic-or-democracy.