What the authors of Out of Many mean by this question is that American society changed in major ways in the 1920s.  We know that the 1920s were a decade in which some people (like the flappers and other city people) became much more modernized while other people wanted to remain traditional.  These are the divisions that are being asked about in the question.  It is asking how the election showed that American society was divided.  In order to find the answer to this question, you must look at the end of Chapter 23 (assuming that the chapter numbers are still the same as in previous editions).  The last subsection is entitled “The Election of 1928.” 

In that subsection, we see that the election of 1928 pitted one of these groups against the other.  The book tells us that native-born Americans were much more likely to vote for Hoover while immigrants voted for Smith.  Protestants, Prohibitionists, small town people, and traditionalists voted for Hoover.  Catholics, people who favored legalized alcohol, big city people and those who were in favor of modern ways voted for Smith.

This is what the authors are trying to get at.  They want to show that this election split along the divisions that had been forming in the US during the 1920s.