Most of the song seems to imply that Shiva was the original, rightful ruler of Ishgard and was in love with a dragon (Nidhogg?), but someone (my best guess is the famed Thordan and his Knights Twelve, possibly being influenced / possessed by the Ascians) did the whole poking out Nidhogg's Eye thing. Shiva then sacrificed herself to try to quell Nidhogg's fury, but those same perpetrators betrayed her and/or the dragons, leading to the millennium-long Dragonsong War.

Midgardsormr implies the Ishgardians are about to do something terrible again, something we (as players) know is likely being influenced by the Ascians. This is implicitly what sparked Nidhogg's reinvigoration of the War, though we don't yet know what that terrible sin is.

I can't quite figure out what the "second verse" means:

Children of the land, answer this
Why must you turn to empty bliss
Tell me why break trust, why turn the past to dust
Seeking solace in the abyss
Tell me why create, a circle none can break
Why must you let go, the life you were bestowed
This I fear I'll never know
Never know
This part's a bit ambiguous, but as it refers to the "children of the land" I'm inclined to believe it's directly addressing the Warrior(s) of Light; specifically, Hydaelyn asking why they're doing what they're doing. Specifically, it seems to ask why we're willing to settle for a hollow, empty victory that perpetuates a cycle; whether she's referring to the Dragonsong War or the overarching Astral / Umbral cycle we can't yet know.