This lesson is significant because of when it occurs in the story, and the example that she tries to use to help define democracy.
First, this lesson occurs after the trial is over and after Scout has noticed Miss Gates' apparent prejudice against the Negro community. Scout overheard some of Miss Gates comments about the Negroes when walking down the stairs out of the courthouse that day of the trial.
Second, Miss Gates lets Scout define democracy and then uses the non-example of Germany. In expressing what Germany does through Hitler, Miss Gates actually described what Scout had seen her do to the local Negro people.
In front of DEMOCRACY, she printed WE ARE A. "Now class, say it all together, 'We are a democracy'."
We said it. Then Miss Gates said, "That's the difference between America and Germany. We are a democracy and Germany is a dictatorship.
“Dictator-ship,” she said. "Over here we don't believe in persecuting anybody. Persecution comes from people who are prejudiced. Pre-judice," she enunciated carefully. "There are no better people in the world than the Jews, and why Hitler doesn't think so is a mystery to me."
In this passage, we see Miss Gates lesson on democracy prove how inept the American south was at applying the tenants of democracy at the time in which Lee wrote.