The arrival of redemption will bring a dramatic and complete transformation for the exiled Israelites. This change will not only remove their physical and spiritual limitations but will also alter the very forces of nature as they make their journey back to Zion.
The primary approach among commentators is that these dramatic descriptions serve as an allegory for the condition of the Israelites during their exile. Currently, the nation is weak and exhausted, moving with the struggle of someone who is lame. They are like a mute person living among enemies, forced to listen to insults and disgrace without the ability to answer back. However, in the future, these exiles will be given renewed strength. They will leap with the energy of a deer, and their mouths will be filled with joyful songs of thanks for God's salvation [רש״י, מצודת דוד]. This sudden burst of energy and leaping is specifically directed toward their journey back to Jerusalem [אבן עזרא]. It is driven by a deep, powerful desire to serve God and follow His commandments, and the joyful singing that breaks out will be directed entirely to Him [מלבי״ם].
The sudden appearance of water breaking through the dry desert is directly connected to this newfound ability to sing. The people's tongues will be freed to burst into song because they will find water everywhere along their journey, a sharp contrast to a state of severe thirst where the tongue sticks to the roof of the mouth [אבן עזרא].
When it comes to the exact nature of this water in the desert, there are two distinct views. Some explain this as a continuation of the earlier allegory. Just as water brings life to a dry and thirsty wasteland, a great and beautiful salvation will suddenly bloom and bring life to the oppressed nation and their land [רש״י, מצודת דוד, ביאור שטיינזלץ]. Others, however, understand this as a literal, physical miracle that will take place in nature. Much like the wonders God performed during the Exodus from Egypt, He will split the earth to create flowing springs and rivers in completely dry, barren places. This miracle will eliminate the harsh dangers of the desert, providing plenty of water for the people as they travel back to Zion [רד״ק, מלבי״ם].