From Wikipedia: http://en.wikipedia.org/wiki/Separation_of_church_and_state
Use of the phrase:
The phrase "separation of church and state" is derived from a private letter written by President Thomas Jefferson in 1802 to Baptists from Danbury, Connecticut. In that letter, referencing the First Amendment to the United States Constitution, Jefferson writes:
Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should "make no law respecting an establishment of religion, or prohibiting the free exercise thereof", thus building a wall of separation between Church & State.
Another early user of the term was James Madison, the principal drafter of the United States Bill of Rights. In a 1789 debate in the House of Representatives regarding the draft of the First Amendment, the following was said:
August 15, 1789. Mr. [Peter] Sylvester [of New York] had some doubts...He feared it [the First Amendment] might be thought to have a tendency to abolish religion altogether...Mr. [Elbridge] Gerry [of Massachusetts] said it would read better if it was that "no religious doctrine shall be established by law."...Mr. [James] Madison [of Virginia] said he apprehended the meaning of the words to be, that "Congress should not establish a religion, and enforce the legal observation of it by law."...[T]he State[s]...seemed to entertain an opinion that under the clause of the Constitution...it enabled them [Congress] to make laws of such a nature as might...establish a national religion; to prevent these effects he presumed the amendment was intended...Mr. Madison thought if the word "National" was inserted before religion, it would satisfy the minds of honorable gentlemen...He thought if the word "national" was introduced, it would point the amendment directly to the object it was intended to prevent.
Madison contended "Because if Religion be exempt from the authority of the Society at large, still less can it be subject to that of the Legislative Body." Several years later he wrote of "total separation of the church from the state." "Strongly guarded as is the separation between Religion & Govt in the Constitution of the United States", Madison wrote, and he declared, "practical distinction between Religion and Civil Government is essential to the purity of both, and as guaranteed by the Constitution of the United States." In a letter to Edward Livingston Madison further expanded, "We are teaching the world the great truth that Govts. do better without Kings & Nobles than with them. The merit will be doubled by the other lesson that Religion flourishes in greater purity, without than with the aid of Govt." This attitude is further reflected in the Virginia Statute for Religious Freedom, originally authored by Jefferson and championed by Madison, and guaranteeing that no one may be compelled to finance any religion or denomination.
... no man shall be compelled to frequent or support any religious worship, place, or ministry whatsoever, nor shall be enforced, restrained, molested, or burthened in his body or goods, nor shall otherwise suffer on account of his religious opinions or belief; but that all men shall be free to profess, and by argument to maintain, their opinion in matters of religion, and that the same shall in no wise diminish enlarge, or affect their civil capacities.
If you take prayer out of schools then the government has interferred with each states right to govern itself. It should be up to the schools themselves, and thus the student body and parents thereof, to determine whether or not prayer should be allowed in their school.
The true purpose is to prevent another inquisition; that is, to prevent a religious person from gaining enough politcal power to make his/her beliefs into laws.