What is the role and significance of Zion in Christianity? The meaning of Zion is uncertain. There is a  hymn related to Zion. The refrain part says,


  We’re marching to Zion,
      Beautiful, beautiful Zion;
      We’re marching upward to Zion,
      The beautiful city of God.


What is the role and importance of Zion in Christianity?
As the Wikipedia article on Zion says, Zion is a synonym for Jerusalem.

Revelation 21 depicts the New Jerusalem, the dwelling-place of God with men:


  21:2And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband; 3 and I heard a loud voice from the throne saying, “Behold, the dwelling of God is with men. He will dwell with them, and they shall be his people, and God himself will be with them. ...” [RSV(CE)]


It is this Promised Land [a similar metaphor] to which Isaac Watts’ hymn refers:


  The hill of Zion yields
  A thousand sacred sweets
  Before we reach the heav’nly fields,
  Before we reach the heav’nly fields,
  Or walk the golden streets,
  Or walk the golden streets.
  
  Refrain
  
  Then let our songs abound,
  And every tear be dry;
  We’re marching through Immanuel’s ground,
  We’re marching through Immanuel’s ground,
  To fairer worlds on high,
  To fairer worlds on high.
  
  Refrain


There’s a Wikipedia article on the New Jerusalem as well.


  Based on the Book of Revelation, premillennialism holds that, following the end times and the second creation of heaven and earth (see The New Earth), the New Jerusalem will be the earthly location where all true believers will spend eternity with God. The New Jerusalem is not limited to eschatology, however. Many Christians view the New Jerusalem as a current reality, that the New Jerusalem is the consummation of the Body of Christ, the Church and that Christians already take part in membership of both the heavenly Jerusalem and the earthly Church in a kind of dual citizenship. In this way, the New Jerusalem represents to Christians the final and everlasting reconciliation of God and His chosen people, "the end of the Christian pilgrimage." As such, the New Jerusalem is a conception of Heaven.