The issue is a little more complex than that, AiiA.  I assume that Devil is referring to the issue of power sharing in a federal system.  The United States was the first government in the world to split power between local and national governments.  Previously, local authorities owed their position to the centralized, national government; thus, they were to be considered appendages of that national government.

In the US, the government's power is split.  Remember that previous to this constitution there was an Articles of Confederation, which allowed the states to act like miniature, independent states.  The EU is a perfect example of a confederation.  This swing from overly centralized to loosely joined caused its onw problems.

Thus, the framers of the constitution tried to accomodate both views.  While the Consitution overpowers the state constitutions, it does so only in areas that are particularly and clearly stated in the document itself.  After that, the States have the remainder of the power.  This is delineated in Amendment X, "The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people."

So, "chunks" of power are provided the Federal government and State governments fill in any gaps.  Until the Civil War, States had significant powers and were largely autonomous in terms of the framework that was set up for its citizens.  That is why slavery was allowed and was only abolished as a result of Amendment XIII.

In all reality, when Amendment XIII was ratified was the last time the spirit of the Federalist system was enforced.  Upon ratification of Amendement XIV, the Federal government was given broad powers to protect the "due process" due every citizen.  ("No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws." )  So, merely by claiming protection of "due process," the National government can invade the areas previously reserved by the states.

This was initially done to protect ex-slaves.  It is now used for a multitude of purposes.  If you like I will continue later and explain various ex cathedra powers of the judicial branch and how it effects the States.

Thanks for the information.  I have to admit, I'm not clear on it myself.  But it seems to me, the US Constitution should override all others within.  Some state constitutions say atheists can't hold office.  I just don't see how states should have the right to shove people out and limit rights when the US Constitution grants them equally.  Like I said, if states can do as they please, what if they all essentially declared inequality, for women, atheists, blacks, the mentally ill, etc.?  Then, what would the US Constitution matter, if it affected nothing?