This edition of Harper's was devoted to "The First Century of the Republic." The map illustrates an article on "Growth and Distribution of the Population," showing the spread of the nation across the continent to 1875.
This map was typical of the period. From the middle of the 19th century, through the fervor of the Spanish-American War, and until the first stirring of World War in Europe, territorial expansion was one of the defining themes of America. The notion of "manifest destiny" supported the acquisition of territory, first across the continent, and then abroad. Maps reflecting and reinforcing those views were "standard fare" in American textbooks, atlases and other works. Schulten 2012, 58, 187-88. The collection includes a number of examples of this “American Imperialism;” see Subjects > Imperialism.