I think I understand what Jefferson (?) meant by it. The original quote is in regard to the intent of the framers of the Constitution, and it says that they intended to “erect a wall of separation between Church and State.” Which means, essentially — since the Constitution necessarily applies to the State only and not the Church — that the government should be “hands off!” with regard to religion. The government should not interfere with the people’s religious practices. This is in two ways: first, there shall be no “state religion,” and secondly, there shall be no law prohibiting anyone from adhering to whatever religion, or lack of any, each one shall choose for himself.
Now, in the practical matter of “how best to govern the people?” the question is bound to arise whether there should be allowed an influence in the other direction, i.e., not that the State might interfere in the affairs of the Church, but that the Church might interfere in the affairs of the State. Where this becomes problematic is where, for example, some group wishes there to be a law, in perfect conformity with their own religious practice, but that might have the effect of curtailing the religious freedom of others.
The United States was founded on the principle of Liberty, and Jesus said, “you shall know the truth, and the truth shall set you free.” So it would seem, initially, that these purposes of State and Church are not at odds. The trouble comes, of course, when there is a plurality of religions. It could be argued that if the only rights at stake are the “rights” of the wicked, the State is under no obligation to protect such “rights.” The very word, “right,” carries with it the connotation of right, i.e. as opposed to wrong. The government is supposed to protect those who seek to do right against those who would wrong them. It is not supposed to protect those who seek to do wrong against those who would seek to correct them; rather, the government is supposed to facilitate that correction.
In the end, Ethics and Politics are very much intertwined, so the question of the proper relation of Church and State is fairly deep.
I keep going back to this, but I highly recommend Pope Leo XIII. In my estimation, he was brilliant.