Direct democracy is where there is direct participation of the people. Everyone would gather in town meetings and vote on issues concerning the town. Since the United States is too big to have such meetings, we instead have representative democracy. Representative democracy, as the name states, is a system in which the people select others to act in their places. For national purposes, we have 2 representatives from each states.
Popular sovereignty means that the people rule.
In other words, the government does the will of the people. Political equality means that each person must carry equal weight in the conduct of the public business. Political liberty refers to the protection of the citizens from the government interfering with basic freedoms, such as freedom of speech, association, and conscience.