The Holy Mountain is something like the center of the world—it's where the magic happens. Technically, in a time and space sense, it's Jerusalem, Mount Zion, location of the Temple. But in the course of Isaiah's prophecies it becomes God's home base, the place everyone, from all the nations, will eventually be forced to turn to when history runs into its endgame.
The Holy Mountain isn't just a place to bring offerings to God for all the nations—though it is that, as well. It's a place where human character and virtue will reach its fullest flourishing. When the hills leap for joy, and the fields "clap their hands" with joy, this natural celebration of the presence of God will have its center in The Holy Mountain where that presence will be fully made manifest.
In one of the Bible's most famous passages, Isaiah 11:6-9, God says,
The wolf shall live with the lamb, the leopard shall lie down with the kid, the calf and the lion and the fatling together, and a little child shall lead them […] They will not hurt or destroy on all my holy mountain.
All violence stops on the Mountain. It becomes the center of a final, ultimate peace that radiates out to the rest of the world, causing all conflict to end totally and filling the world with righteousness and the knowledge of God.