A very important concept
outlined in the First Amendment
of the Bill of Rights
in the US Constitution
Simply put, it means that the government will have absolutely nothing to do with religion. It will neither support nor supress any set of religious beliefs. It will remain completely neutral. The lack of mention of the word God in the Constitution is good evidence in this favor - as it was common to mention God in just about every legal document at the time - all of the state constitutions before the USA was formed not only mentioned God, but made their beliefs clear in those documents. The total exclusion was highly unusual at the time.
Also see the Letter to the Danbury Baptists.
Some have suggested this term is not accurate enough, and should be changed to fit the words of James Madison, as "separation of religion and government".
Many of the Religious Right believe that seperation doesn't/shouldn't exist, or claiming it was only to prevent a national church from being set up - however, if this was intended, why did they, during the debates when creating the Bill of Rights, reject that wording?
Is it possible to have Christian control over government and not have governmental control of Christianity in return? If religious belief exerts control over laws and decisions of the government, then you're controlling which form of religious belief is acceptable. If the government passes a law making something considered bad by one religion illegal, then any other religion in that country is then bound by that law - and a religion that considers that action good is no longer free, and is being controlled by the government.