The "Establishment Clause" of the US Constitution represents the first amendment made to the US Constitution. Wikipedia provides a summary of its intent and meaning:
In United States law, the Establishment Clause of the First Amendment to the United States Constitution, together with that Amendment's Free Exercise Clause, form the constitutional right of freedom of religion. The relevant constitutional text is: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof...".
The Establishment Clause was based on a number of precedents, including the Constitutions of Clarendon, the Bill of Rights 1689, and the Pennsylvania and New Jersey colonial constitutions. An initial draft by John Dickinson was prepared in conjunction with his drafting the Articles of Confederation. In 1789, then-congressman James Madison prepared another draft which, following discussion and debate in the First Congress, would become part of the text of the First Amendment of the Bill of Rights. The second half of the Establishment Clause includes the Free Exercise Clause, which allows individual citizens freedom from governmental interference in both private and public religious affairs.
The Establishment Clause is a limitation placed upon the United States Congress preventing it from passing legislation forcing an establishment of religion. The second half of the Establishment Clause inherently prohibits the government from preventing the free exercise of religion. While the Establishment Clause does prohibit Congress from preferring or elevating one religion over another, it does not prohibit the government's entry into the religious domain to make accommodations for religious observances and practices in order to achieve the purposes of the Free Exercise Clause. Furthermore, it does not prevent the placement of religious symbols on government premises.
In recent decades non-establishment has come to mean that the State is required to be functionally atheistic.

