It's an American concept coined by Tommy Jefferson to express the idea that in America, unlike many of the European nations to which they left, the state would not hold power over the church. There would be a "wall of separation between church and state" such that the state could not meddle where it didn't belong. Of course, those within the church were allowed to provide input into the government (just as those outside the church could do).
Modern secularists on the left have twisted the meaning around to say that the church cannot hold sway over the government, but the state can reach through the veil of separation to control what the churches do.