"an establishment of religion"

This is perhaps, one of the least understood phrases in the Bill of Rights. Notice, please, that it does not say "Separation of Church and State." These two concepts are related but are not the same thing.

To put this phrase in context, at the time England had a state religion. Everyone was officially a member of The Church of England (The Anglican Church). Whether you were Catholic, Deist, Whatever, you were officially part of the King's Church. The King (now Queen) is the head of the church, much as the Pope is the head of the Catholic Church. One of the great things about the British Colonies in America is that in most colonies you could belong to whatever religious group you chose. Many colonists came to America to escape religious persecution. Remember the Pilgrims? They would not follow the teachings of the Church of England and were persecuted for their Puritan beliefs. Quakers, Catholics, Mennonites and Amish, Puritans, and others all emigrated here to be able to exercise their religion freely.

Philisophically, the founders did not want to establish a religion. Because America was formed in a climate of religious tolerance, the very idea of imposing a set of beliefs on the populace was abhorrent. Even if the government were to establish a State religion, whose would it be? It couldn't be the Church of England, because that would put them under control of the King again. What religion would they pick? Anything would put some out in the cold. So, logistically it wasn't even possible.

As a matter of fact, in order to fully break ties with England, the Anglican Church was dissolved. Priests of the (then) Anglican Church took their authority from the Scottish Episcopal Church (in Scotland). This church follows the same beliefs, rituals, and structure as the Anglican Church, but the King is not its head. That is why today in America you can attend an Episcopal church, but will have a hard time finding an Anglican one.