A government of laws, not of people: Under a government of people, whatever party holds the reigns of government, has as a guide for its conduct only its own judgement, wishes, or whims. Whatever it dictates, is law.
Under a government of laws, the party that is in power must obey the laws that exist, the same as the rest of the people, and the laws must be passed by a prescribed procedure: if the parties not in power can hold it (the party in power) to the deal.
The framers of our Constitution tried to ensure that our government would be a government of laws. First of all, they made a written constitution. Having our principles of government in written form holds always before the party in power a sort of moral restraint concerning what it is supposed to do and what it is not supposed to de. Having a written constitution also serves the parties not in power (including the common citizens) in that it gives them something to hold forth as an example of how they should be treated. If they appeal to either their governors, public opinion, or the courts, they can cite principles in the written constitution. The Bill of Rights of our Constitution is very important from the standpoint of always keeping before both the rulers and the ruled, the principles of our government.
Second, the framers provided that the three branches of our government (executive, legislative, and judicial) would be separate in that no one person may serve simultaneously in two or more of the branches. Therefore, each branch serves to check the activities of the other two. This serves as a curb on serious abuses of governmental power. Also the powers given to each branch do not much overlap. The judiciary can only judge; it cannot legislate or execute. The legislature can only legislate; it can neither judge nor execute (except that in Reconstruction, it did). The executive cannot judge, but does participate in the legislative process, though never independently, always with the legislature (if you don't count executive orders, but how can you not count them). This is not as good of a curb as it might be, because all three branches are chosen by the same constituency, the democratic majority. If each were chosen by separate constituencies, such as wealth, population, and education, the separation of governmental branches would be a better protection of the citizens' rights.
Under a government of laws, the citizens have a pretty good idea how they will be treated from day to day and in response to whatever action they each or in groups might perform. the laws can be read and understood. Under a government of people, the citizens are at the mercy of governors who are not guided by laws and so may treat the citizens arbitratily; the citizens do not know what to expect; life is uncertain for them; is it safe to enter into a business, or will the governors decide they don't like my type of business? Will the governors give a monopoly of all of my type of business to their special friends? And so on.
The system that the Constitution sets up is one based on ideals, principles, goals, and laws. I think that the reason this is great is because it does not depend on people and individuals. History has shown us that a government based on the charisma of individuals can lead to disastrous policies and treatment of individuals. The Constitution's strict adherence to laws helps individuals fit within this configuration of government, and not allow them to supersede it. The consistency of a government of laws helps to ensure that the portions of individual nature that might be predisposed to committing acts of cruelty or inhumanity are kept in check precisely because of this government of laws.
The purpose of the U.S. Constitution was to create a 'more perfect' union. The founding fathers of the Constitution accomplished this task by establishing the framework of how the new nation's law would be structured. Having said that and to address your statement, the Constitution sets up a framework of law based upon the principle that no one is above the law...not even the people. Therefore your statement is valid because it suggests that the law is supreme and the people are subject to it.
What this means is that the laws set out by the Constitution are what govern our society. This is in contrast to systems that had a strong monarch where the king or the queen could do whatever they liked.
A system of laws in one in which everyone must obey the laws and the laws can only be changed in a manner spelled out by law. No one person can change the laws. We have a system that is like that.
In old-style monarchies, the monarch was above the law. He or she did not need to obey it and the monarch could change the law just because he or she wanted to. That's why that would be a system of people -- because a person could do whatever they want, not what the laws tell them to do.
A constitution is a set of rules or laws that provides the overall framework for governance of the country. Whether a country is democratic or not is determined by the nature of the constitution. In a truly democratic country the constitution is made keeping in view the interest and good of the people, and the people have substantial influence in amending or improving the constitution. But people do not have the power to bypass or overrule the constitution in force.
A country is governed by the constitution and the laws that are created to implement the constitutions, and that conform to constitution, not directly by the people. This just like saying that the it is the knife that cuts, and not the hand that holds the knife.