Article Six addresses various other items that were of a concern with creating a new constitution and a new Federal government.
Clause 1: The US will still honor its debts.
There was some concern that with a new constitution/government that the US wouldn’t honor debts or contracts entered into under the Articles of the Confederation (The First constitution that the United States had ratified). The first clause addresses this concern by saying that the Constitution will uphold anything debts that occurred or engagements (such as treaties and contracts) shall be continued under the new constitution.
Basically it means that the US is under new management, but the old deals still apply.
Clause 2: The US Constitution shall be the ultimate law of the land.
This directs that any law, judgement or other actions by the government must adhere to this document. It also states that all states are subject to the Constitution and Federal law, effectively bringing them under the same umbrella. One of the ongoing issues with the Articles of Confederation was the lack of power the federal government had to do anything. The confusion as states formed their own money etc couldn’t be corrected by the federal with much power behind it. This government however was stronger, and made sure to specify that this document was the supreme law. This also effectively transitions the country from working under the Articles of Confederation to having a new constitution.
Clause 3: All officers of the government shall uphold the oath. None of them will be forced to prove their religious faith.
There are two elements to the third clause. One is that every officer of the government is to swear an oath of allegiance to uphold the constitution when taking office. The other element is that no officer has to prove his religious choices to get into office.
This particular element has come under recent speculation, This clause basically assures that there is no government backed religion, that no person who works in the government will have to prove their religion in order to take office.
With fundamentalism of many religions being more visible, many people are being asked unofficially to prove that they belong to one religion or another. Personally I believe that this clause in the Constitution makes it unconstitutional to make someone prove that they are part of a religion (regardless of said religion) in order to do their job (i.e. take office), or seek services from the federal government. Many have alternate points of view on the subject.
The Supreme Court expanded this clause to the states in 1961’s Torcaso v. Watkins. Now no governmental employee, federal, state or otherwise, is required to prove one’s religious conviction or religious orientation to take office.
I found Heritage Guide to the Constitution had an interesting background for this particular clause (I’ve included the link below in the further reading) which also goes into people’s concern about secular language (a argument still had today).