The entirety of creation is invited to participate in a profound celebration over the redemption of the Israelites. The heavens and the earth are called upon to sing and rejoice, serving as a vivid metaphor for the overwhelming happiness that will fill the world, as if the universe itself is celebrating the end of the Israelites' exile [רד״ק, מצודת דוד]. This deep joy is a direct response to God's abundant kindness and mercy in redeeming the multitudes of His people [חומת אנך]. However, this celebration can also be understood as more than just a metaphor. It may describe a tangible, physical transformation within nature itself. In this view, the singing of the heavens means the air will become completely pure and clear, while the joy of the earth and mountains will take the form of producing abundant crops [אבן עזרא].
As the call to celebrate echoes through nature, the mountains are specifically urged to break into loud, intense song [מצודת ציון, רד״ק]. Even though mountains are inherently part of the earth, which has already been called to rejoice, they receive their own distinct invitation. This is because mountains represent the most permanent, central, and foundational elements of the earth's creation, holding precious metals within them [רד״ק]. Furthermore, singling out the mountains highlights that the good news of redemption has traveled all the way to the most distant, isolated mountain dwellers, inspiring them to join the global chorus [מלבי״ם].
Ultimately, the cause of this worldwide rejoicing is the comfort God brings to His people [רש״י, ביאור שטיינזלץ]. He has witnessed the deep suffering of the poor and oppressed who were exiled in the furnace of poverty, and He has extended His mercy to them [מלבי״ם, ביאור שטיינזלץ].