The Supremacy Clause is the sixth article of the Constitution of the United States. It reads:

"All debts contracted and engagements entered into, before the adoption of this Constitution, shall be as valid against the United States under this Constitution, as under the Confederation.

This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding.

The Senators and Representatives before mentioned, and the members of the several state legislatures, and all executive and judicial officers, both of the United States and of the several states, shall be bound by oath or affirmation, to support this Constitution; but no religious test shall ever be required as a qualification to any office or public trust under the United States."

Simply stated, it means that Federal law is the "supreme law of the land," and that no state, local, or other law can countermand anything stipulated in the constitution. An example: It is a federal law that Marijuana is illegal; however, if there is a state which stipulates that Marijuana is legal, the federal law is supreme, and Marijuana, for all intents and purposes, will be considered illegal.

See also McCulloch vs. Maryland


Source: http://www.law.cornell.edu/constitution/constitution.articlevi.html