In "The Pilgrim"s Progress", written by John Bunyan and published in 1678, The Celestial City is the "Desired Country" of pilgrims, heaven, the dwelling place of the "Lord of the Hill", God. It is situated on Mount Zion. So another way of saying it is "heaven" or "Heaven" or City of God.
I do not know how widespread this awareness of the phrase now is in the English-speaking world, but all those who have been to a Church of England school or brought up in a Church of England family, would know of the book The Pilgrim's Progress and therefore The Celestial City. I would imagine that it is in the general studies or literature syllabus of most secular schools as well.