What does it mean?
It means that the State is to have nothing to do with the enforcing of religion by its laws or restricting religion by its laws and that the Church is not to go to the State to have its religion/beliefs enforced by State Law. It doesn't mean that the State cannot involve itself in religion and practice religion - it is only prohibited from enforcing religion or the lack thereof by law.
The first amendment of The Bill Of Rights of the United States of America states that "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances."
Does this mean that the State can't practice, encourage, and or support religious beliefs? No, it doesn't mean that. It means that it is not to make laws respecting religion and religious beliefs; the establishing of or the prohibiting of religion. They can encourage or discourage religion all they want, as long as they don't make laws to accomplish it. The government is not to have any strings attached to any help they give. Whatever is given must be "Freely" given by the government. At the same time, Religious groups are not to solicit government support in any way.
Liberals have, are, and are pushing to make laws that prohibit religious practices and beliefs. This is totally going contrary to the first amendment. There is nothing in the Constitution or Bill of Rights that states that there is to be a separation of Church and State. It simply states that the government is to make no laws having to do with the establishment of religion, or prohibiting the free exercise of religion. Although neither the Constitution or Bill of Rights refers to the a separation of Church and State, the principals regarding it are definitely there.
In conclusion, the laws and bans that prohibit the free exercise of one's religious beliefs are in violation of the first amendment and are contrary to everything that the Founding Fathers of the United States of America stood for and believed.
For more insights on this topic see: "What's Going on in America?"
2 Timothy 2:15