Why is the Constitution important and how does it work?

The United States Constitution is the document that set up our entire system of government.  It tells us the distribution of power amongst the three branches of government and the distribution of power between the federal government and the state governments.  It sets forth the rights and duties of federal government.  It also sets forth the ways that Americans are protected from the government.  In some ways, it could be thought of as the Bible of American government.  It has, in my opinion, created the most successful democracy of all time, recent and current events notwithstanding.
The way the Constitution works is that anyone who thinks that the government is acting in a way that violates it has the right to go to court and seek relief from that violation.  Sometimes it is one branch of government accusing another branch of government of violating the Constitution. Sometimes it is a private organization or a private citizen making that claim. The court decides whether or not that is the case, and if someone in government is violating the Constitution, he or she is ordered to stop doing so.
The court must read the Constitution and interpret it to apply to the case at hand.  Reading it literally is often of no use.  For example, there is nothing in the Constitution that says Congress is supposed to fund interstate highways.  There were no interstate highways when it was written.  But the Constitution has been interpreted to mean that Congress can do this because it is part of our national defense, which Congress is constitutionally responsible for.   In this way, too, the Constitution is like the Bible.  For instance, there is nothing in the Bible about cars, yet observant Jews will not drive on the Sabbath because that has been interpreted to be a form of work, which is forbidden on the Sabbath.  Any document must be read in accordance with the time and place it is meant to be applied to.
I should also say that the Constitution is to some degree a kind of social contract.  The courts do not have soldiers to enforce their orders.  We all agree to abide by the Constitution in order to live in a civilized democracy.  If that social contract breaks down, for example, if a president refuses to abide by a constitutional ruling by the court, the nation and the Constitution are in a great deal of trouble.