Article Six of the United States Constitution says that the Constitution, and any laws or treaties the United States might make, will be the most important laws in the United States.  It also says that the United States will pay debts from before the Constitution was written.  Finally, it says that members of the United States government have to swear that they will obey the Constitution.  However, they will never have to swear that they follow a certain religion.

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Debts
Before the United States Constitution was written, the United States had another constitution called the Articles of Confederation.  The Articles made the states into a Confederation.

The first part of Article Six says that the United States will still honor and pay all of its debts from before the Constitution was written.  The Article says that "these debts are as valid against the United States under this Constitution, as [they were] under the Confederation [governed by the Articles of Confederation]."

Supremacy
The second clause of Article Six is often called the "Supremacy Clause."  It says that these things are the "supreme" laws in the United States  the most powerful and most important laws in the country:
 The Constitution
 Laws made by the United States government
 Treaties made by the United States government

Because these laws are supreme:
 State courts have to follow them
 States' constitutions are not as powerful as the United States Constitution
 If there is a disagreement between a federal law and a state law, the federal law is more important.  The federal law must be used.
 Even the President of the United States has to obey the Constitution. 

For example, part of the Constitution called the Bill of Rights gives people the right to freedom of religion.  Because the Constitution is the supreme law of the land:
 No state court could rule that a person could not practice their religion
 No state constitution could say that certain religions are illegal in that state
 No state could make a law that said people could only practice certain religions
 Even the President could not refuse to hire people for his government because they don't practice his religion

Later in history
A few Supreme Court decisions helped make the Supremacy Clause clearer.

The first important case was Marbury v. Madison (1803).  In this case, the Supreme Court ruled that it had the power to review state courts' decisions, if those decisions seemed like they did not follow the supreme law.  This power is called judicial review.

In Martin v. Hunter's Lessee (1816), the United States Supreme Court ruled that it was more powerful than the state Supreme Courts.  In the case, the Virginia Supreme Court said that a United States Supreme Court decision was unconstitutional, and told all of the Virginia state courts not to obey it.  The United States Supreme Court ruled that it had the final say in legal issues that had to do with federal laws  not the state courts.  If a state court and the United States Supreme Court disagree, the Supreme Court is the supreme law of the land.

Three years later, in McCulloch v. Maryland (1819), the U.S. Supreme Court ruled that states cannot control federal institutions.  The state of Maryland had tried to tax a federal bank.  The Supreme Court ruled that states cannot tax government property.  This was another example of a case where the U.S. Supreme Court decided that the "supreme laws of the land" were more powerful than state laws or court decisions.

In 1824, the Supreme Court ruled on Gibbons v. Ogden (1824).  The state of New York had given Aaron Ogden a monopoly over the steamboat business in the Hudson River.  However, Thomas Gibbons got the same power from a federal government permit.  The Supreme Court decided that the federal permit was more powerful than the state monopoly.  Supreme Court Justice John Marshall wrote: 

Finally, in Reid v. Covert (1957), the U.S. Supreme Court ruled that no branch of the United States government can be given extra powers by a treaty, if those powers were not given to it by the Constitution.  This case showed that the Constitution could even limit the power of treaties, and was truly the supreme law of the land.

Oaths
The last part of Article Six is sometimes called the "No Religious Test Clause."

This clause says that people have to swear to support the Constitution if they are:
 Members of the United States Congress
 Members of state legislatures
 The President, Vice President, and the people who work for them
 Judges

Congress gets to decide the exact words in this oath to support the Constitution.  However, in this oath, they cannot require a "religious test."  This means they cannot make a person swear that they follow a certain religion.

Under this clause, Congress may include the words "so help me God" in the oath.  However, a person cannot be required to say those words.  A person cannot be required to swear or say anything about religion in order to work for the United States government.

Later in history

During the 1960 presidential campaign, John F. Kennedy was running for President.  If he were elected, he would be the first Catholic president ever.  Many people were unsure that Americans should elect a Catholic as president.  This raised the question of whether Americans  not their government  were requiring a "religious test" for their President.  Would they require that a President be a Protestant in order to get elected? 

On September 12, 1960, Kennedy talked about this issue directly in his Address to the Greater Houston Ministerial Association:

Kennedy won the election.

Related pages
 Separation of church and state
 Judicial review

References 

United States Constitution