The call is for the heavens and earth to joyfully sing because The Lord has comforted Israel. The suffering of the exiles would one day end for the Jewish people. They would return again to their own land and most importantly, to their own God. This would be a cause for great celebration.
This is a post-exilic celebration promise given well before Judah even went captive to Babylon. The nation is on the cusp of collapse. Isaiah has warned them that Babylon's forces will invade. But God has also named Cyrus as the ruler who will return them to Jerusalem again. God predicts the joy of the return before even one invader's arrow has nicked the walls of the city.
God is a God of justice. And our sins will thus pain us when His justice must correct us. But He is also a God of comfort. And this passage shows us His comforter's heart. He will see us in our afflictions. He will love us. He will restore us.
This was a specific comfort to Judah. It is a general truth for God's people today. We can be encouraged by the work of redemptive history. We can find comfort and compassion in Christ. God loves us in His Son. He comforts us by the atoning work and resurrection of Jesus. He has compassion on our afflictions. And we can sing with that truth bolstering us.