the image's feet and toes show there will be another kingdom which is part iron and part clay."
These represent the two types of governments the World has known since the fall of Rome; dictatorship & Democracies.
Clay in god's Word always symbolized the people. As Isaiah 64:8 says, "We are the clay."
So government by the people, or democracy, is a "clay" government. They are a weaker form of government because they do not have "the strength of iron", which represents the strong-man totalitarian military dictatorships & their "iron" rule, which usually have an "iron man" as their dictator.
As you remember, one foot comes out the Western Roman Empire & one foot out of the Eastern. This is almost exactly how the World is divided now.