Originally written by Thomas Jefferson in 1802, the phrase "Separation of church and state" was enshrined into US law during the Supreme Court ruling on Everson v. Board of Education in 1947.
"The 'establishment of religion' clause of the First Amendment means at least this: Neither a state nor the Federal Government can set up a church. Neither can pass laws which aid one religion, aid all religions or prefer one religion over another. Neither can force nor influence a person to go to or to remain away from church against his will or force him to profess a belief or disbelief in any religion. No person can be punished for entertaining or professing religious beliefs or disbeliefs, for church attendance or non-attendance. No tax in any amount, large or small, can be levied to support any religious activities or institutions, whatever they may be called, or whatever form they may adopt to teach or practice religion. Neither a state nor the Federal Government can, openly or secretly, participate in the affairs of any religious organizations or groups and vice versa. In the words of Jefferson, the clause against establishment of religion by law was intended to erect 'a wall of separation between Church and State.'" 330 U.S. 1, 15-16.
A similar ruling was made in 1879 in the Supreme Court decision in Reynolds v. United States, where Chief Justice Morrison Waite wrote the unanimous decision of the court. Jefferson's comments in his letter in 1802 "may be accepted almost as an authoritative declaration of the scope and effect of the [First] Amendment."
Both of these rulings dealt with public figures attempting to force religion into the state sphere of the United States. Reynolds was a Mormon polygamist who lost his appeal every step of the way to the Supreme Court arguing that his religious beliefs were above the laws of the country even though the First Amendment states "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof." The Supreme Court ruled that the intention of the First Amendment did not allow private religious citizens to break the law to practice their beliefs.
Everson v. Board of Education argued that private religious school students should be given taxpayer funds to ride public transportation for free to school. Their argument was "but the public school students get free rides, why not the private religious schools?" The answer was that the public school system is a product of the United States government while the private religious schools were not because of the First Amendment.
There are other decisions that further enshrine the separation of church (meaning religious beliefs and practices) and state (meaning institutions of the government, such as public schools). Hence, when a principal decides he's going to hang a big old portrait of Jesus in a public school and say its his First Amendment right to publically display religious artifacts in a government-funded public school, he is violating the separation of church and state established in the First Amendment, originally defended by Thomas Jefferson and enshrined into law in his exact language in 1947.
Everson v. Board of Education