Here is a really good Prager explanation of what a Constitutional Republic is...
Robert P. George | Princeton Politics
If you need a meme to summarize the concept, I like to use this one...
The importance of a Republic, is that there are certain rights that each citizen should have, that the government or rich business owners, can't take away. Regardless if the majority of the people want to take them away. A very good example of this, shocked the conscience of America and the world, but in hindsight, proved what makes this country the best in the world.
Here is an excellent Quora answer on why the pardon of President Nixon was the right thing to do.
Here is a great article about the pardon of Richard Nixon.
The Nixon pardon in constitutional retrospect - National Constitution Center