Also found a non Facebook posted version of the light novel the fight happens in, turns out it was 20,000 people left in the army (it had been 30,000 but Asuna and them had managed to kill 10,000) buuut that's the less important issue.
So the silver light that the ice roses send out after Kirito activates them was born from the HP being drained from said army, Asuna recognized it as "life resources" but more specifically its explained by Kirito's juniors from the swordsmanship school that the light is Sacred Power, or the "Life Resources" of the Sun and Earth that the Gigas Cedar the Night Sky Sword was made from survived and thrived on.
As Volume 18 Ch 21 puts it
However, Kirito’s black sword was different. Since it was originally a tree surviving off the power of the earth and sun, then both sword and wielder should have imagination powerful enough to absorb life.
His god-tree sword eats Spirit Bomb juice. That...actually probably explains why it was able to eat a solar powered death ray. Yeah that also means the life force of people without killing them, but...it can just passively absorb that shit if Kirito believes hard enough via his Underworld Avatar's...memory/belief/imagination power.
But yeah Incarnation attacks are basically "clap your hands if you believe" cranked to 11
If one were merely comparing the amount of resources stored in their weapons, then Kirito’s black sword having absorbed the lives of 20000 people, far exceeded PoH’s Mate Chopper without question. But the situation was not that simple. In this world, imagination… «Incarnation», as the knights called it, bore with it the possibility to overturn any numerical specifications.
Buuut yeah, Kirito can just absorb the ambient life energy of the universe?
Edit: Oh, also he can fly. Without wings....and locate specific individuals with his mind.
Kirito exchanged a close look with Asuna, nodded, then turned his eyes towards the southern sky.
He raised his right hand in that direction. His five fingers moved, seemingly searching for something.
“…… Found them.”
“Huh…?”
Asuna blinked, but Kirito did not reply; he simply revealed a hint of a smile.
Surveying the crowd once more, Kirito gently patted Klein’s shoulders and Ronye’s head before saying:
“Well, here we go.”
And then—
***
And then Lisbeth watched as Kirito and Asuna were enveloped in bright green light and took flight at extraordinary speed towards the south.
She blinked her wide eyes a few times, then dragged out a long sigh.
“Good grief… Always going too far. Or maybe I should just call him reckless…”
Silica chuckled from aside.
Klein clapped his hands together loudly and bellowed.
“Wait one minute, goddammit… Is that bastard ******? Isn’t he unstoppable now? Goddammit, he always steals the show…”
The katana-wielder groused, his cheeks shining with renewed tears, uttering the name of the male protagonist from a very old manga. To him, Kirito must have always been that kind of person he had been enamored with, ever since they had first met in Aincrad. An unstoppable, absolute, eternal hero.
─And he’s the same to me.
Edit2:
Explanation of how that is possible
Gray clouds raced past me and Asuna at incredible speed. The blood-red sky overhead and jet-black wilderness underfoot expanded as far as the eye could see.
There’s only one person capable of the Art of airborne flight in all of the vast Human Empire, and that’s the Highest Minister ─ Integrity Knight Alice once told me. Since Highest Minister Administrator and her «counterpart», the sage Cardinal, had both left Underworld, there was no way to find out exactly how they had learned the Flight Art. That’s why it struck me that my ability to fly in midair above the Dark Territory like this had nothing to do with an Art, but was the result of me directly manipulating things with my imagination… the power that the Integrity Knights called «Incarnation».
Cardinal’s familiar Charlotte had protected me ever since I’d left Rulid Village, and right now I could hear the giant spider’s words once more, deep in my ear.
—Every single Art is naught but a tool to guide and tweak your Incarnation… your imagination, as you call it. You don’t need incantations or mediums anymore.
—Now, dry your tears, and stand up. Then, feel them. The prayers of the flowers.
—The truth of the world.
In the time that I shut myself out of the world around me after the battle with Administrator on the topmost floor of the Central Cathedral of the Axiom Church, all the way until I recovered a few tens of minutes ago, I seemed to establish an incredibly deep connection with the «truth» of this world.
I could feel, quite clearly, the Sacred Power swirling in the space around me, and I could convert it, quite easily, into elements without the need for an Art. Although I had used an incantation when I had healed Klein and Lisbeth’s Life back there, I should have been able to achieve the same effect just with my imagination.
Right now, I was flying by covering mine and Asuna’s bodies with Aerial Elements to counteract air resistance while continuously discharging Aerial Elements behind us like a jet engine. We were several times faster than a dragon, but we still needed at least five minutes or so before we could catch up to Alice and the dragon she was riding towards the far south, Amayori.
