A couple of generations earlier, their country had been invaded and their capital destroyed. Many of their grandparents would have been swept into exile. The central place of worship, the place where they sought reconciliation with God, was destroyed.
Isaiah is speaking to the exiles, "Listen to my words. Look to the rock from which you were hewn."
To see what can happen, we look back at what has happened.
Isaiah continues, "Remember your ancestors, Abraham and Sarah; remember how, under God's call, they thrived." Abraham and Sarah traveled from home to a strange land. The promise of progeny was long delayed but realized. The God who called them, nurtured them, accompanied them, is the God who is now offering comfort to the exiles.
Even earlier ancestors, Adam and Eve, lost Eden because of their disobedience. Isaiah is now promising that their descendants will migrate in the opposite direction. The wilderness will become Eden (51:3).
For more background on this passage, look back at Isaiah 49-50.