Social foundation refers to social status, class, social groups, etc. Or the cultural basis, that is, value standards, spiritual temperament and cultural types.
"Expanding the political foundation" here means that the imperial examination system has provided a large number of talents for the ruling class. On the one hand, their political identity will be more inclined to the ruling class, on the other hand, it also provides new ideas for the political perspective and culture of the ruling class.
"Expanding the foundation of anti-fascist society" means that the United States was an important force in the world at that time. When the United States entered the war, people's confidence was greater and their strength was certainly stronger. The cohesion and centripetal force of the World Anti-Fascist Alliance have been significantly improved. Of course, it can also be directly understood that the United States' participation in the war represents the entire American nation, and at the same time it also drives countries that hate American culture to participate in the war formally or informally, thus expanding the social forces against France and West in the world.