The part of the U.S. constitution that subordinates laws of the states to those of the Federal government, and to the Constitution itself.

To most of the people who've ever heard of it, and to those that make up the legislative and executive branches of the federal government, and to the nine wannabe gods in their attractive black robes, who know better but don't care because they have their own agendas, it simply means that the Congress can pass any law they want to and, if the President goes along with it, can remake the face of the country in accordance with their sublime wisdom and paternal oversight of their 250 million chillun.

The ignored part of the clause is noted in this snippet:

This Constitution, and the laws of the United States which shall be made in pursuance thereof,
People who realize that most of the federal laws in existence are unconstitutional would also realize, upon minimal reflection, that the purpose of the supremacy clause was simply to preserve the structure and integrity of the union that the states (as those nations were referred to) had entered into, not to convert them into the mere organizational units that, for all intents and purposes, they are now.

Thus, as noted in an earlier writeup as an example of supremacy in action, federal drug laws, which the Congress has no right to pass, are allowed to trump those of the states.

But, ever since The United States of America started becoming a singular term, rather than the plural which it was before the Civil War and which denotes the polity that the Founding Fathers intended, the people of this country have been educated that the Federal government is the government; a mindset perpetuated, not only by such disinformation but also by the steady accretion of more and more unconstitutional programs by that government.

This weltanschauung is what leads to agents of the FBI, the DEA, the BATF, and other unconstitutional federal policemen being received with bowing and scraping, sometimes accompanied by subvocalized grumblings, by the local police when they show up at a crime scene and take over, citing higher jurisdiction.