There are several forms of government that are possible: Dictatorship, Socialism, Nazism, Fascism, Democracy, Republic, Oligarchy, Monarchy, etc. When we break them all down though, there are essentially two sides to the issue. There is Ruler's Law and People's Law. On the extreme or Ruler's Law, we have all of the totalitarian governments: Nazis, Fascists, Communists, etc. On the extreme of People's Law, we have Democracy and Anarchy. Yes, I just linked those two together. Why is that? Well, the classic example of a Democracy is "mob rule." Here, the majority wins... no matter what. The Founders were afraid of a Democracy and realized that the will of the people is subject to sudden changes in opinion and needs to be moderated. They were against a Democracy, and if you scan through the Constitution and Bill of Rights, the word never appears. The Founders never intended to form a Democracy. Remember the Pledge of Allegiance? It specifically says "And to the Republic for which it stands." Our country is meant to be a Constitutional Republic! Is this all just semantics? No. There is a distinct difference. A republic is controlled by laws and the fragile public opinion is kept in check. That is why it is so hard to amend the Constitution. That is why everything takes more than just a 50% vote in Congress to pass. It is the same reason we have checks and balances. It is supposed to be hard to get things done in Washington so that we do not do something on a whim and then regret it.

A constitutional republic is a state where the head of state and other officials are elected as representatives of the people and must govern according to existing constitutional law that limits the government's power over citizens. In a constitutional republic, executive, legislative, and judicial powers are separated into distinct branches so that no individual or group has absolute power and the power of the majority of the population is checked by only allowing them to elect representatives. The fact that a constitution exists that limits the government's power, makes the state constitutional. That the head(s) of state and other officials are chosen by election, rather than inheriting their positions, and that their decisions are subject to judicial review makes a state republican.

These paragraphs from Wikipedia sum it up better than I could:

Note that the US Constitution states that the power comes from the people "We the people..." However, some argue that unlike a pure democracy, in a constitutional republic, citizens in the US are not governed by the majority of the people but by the rule of law. Constitutional Republics are a deliberate attempt to diminish the threat of mobocracy thereby protecting minority groups from the tyranny of the majority by placing checks on the power of the majority of the population. Thomas Jefferson stated that majority rights cannot exist if individual rights do not. The power of the majority of the people is checked by limiting that power to electing representatives who govern within limits of overarching constitutional law rather than the popular vote or government having power to deny any inalienable right. Moreover, the power of elected representatives is also checked by prohibitions against any single individual having legislative, judicial, and executive powers so that basic constitutional law is extremely difficult to change. John Adams defined a constitutional republic as "a government of laws, and not of men."

The original framers of the United States Constitution were notably cognizant of what they perceived as a danger of majority rule in oppressing freedom and liberty of the individual. The framers carefully created the institutions within the Constitution and the United States Bill of Rights. They kept what they believed were the best elements of majority rule. But they were mitigated by a constitution with protections for individual liberty, a separation of powers, and a layered federal structure. Inalienable rights refers to a set of human rights that are not awarded by human power, and cannot be surrendered. The Constitution of the United States was written to protect the inalienable rights of citizens from potential excesses of government, even if taken by majority rule. Inalienable rights are not granted by government, but by nature.