I've written up some thoughts on The Orb. For best ambience, please listen to theholelol.mp3 on loop while reading this post.
View attachment theholelol.mp3
Someone already pointed out the orb appears in Ayane's picture from the fifth reset. It also shows up in "The End of the Tour" when Sensei is blocking out the accident, and he sees a sakura tree inside of it.
In Sensei Quest, Meowri creates the orb after a car crash. When you put these together, it seems likely to me that the orb was created when Sekai was killed in the accident. My guess is it's the manifestation of Akira's feelings of grief and guilt, and desire to punish himself for not preventing her death by leaving with her - which is consistent with Meowri calling it the dark entity inside of him.
In the fifth reset photo, the orb is in the place where the moon should be. During the reset itself, there's a red moon and Kaori is on the roof wearing Sekai's dress (identified by the nail polish).
So the orb is a black void where a moon should be - probably the moon that Ami wants to use her wish to bring back. We've theorized before that moon is the real Sekai, which seems consistent with the other appearances of the orb.
SeKaori says that bringing the moon back would require rewriting history, i.e. preventing the accident or at least Sekai's death.
As chronox pointed out, the orb's name changes to GOD when it's consuming Sensei.
It's a GOD that is composed of four parts and came into being after a car accident. The narration from "First Contact" also talks about the USER gods being created by a (possibly metaphorical) car crash.
It's also likely that it has something to do with the thing that sings in its sleep, which is missing the orb meant to guide it and has something to do with a god that encompasses everything. This is from an event in the same update as "First Contact" and they both use itsingsinitssleep.mp3
Later we're told it's the middle of the four-sided cross, i.e. it encompasses all four gods.
What I'm unclear on is whether the orb is itself that thing that sings in its sleep - in which case the orb that's supposed to guide it is the missing moon - or if this means that the returned orb is going to wake some other sleeping entity.
John might have warned about the orb in "Sasom i en Spegel". He talks of a dead god that will return after the death of someone of equal value, which is very similar to how SeKaori describes the return of the moon.
Just before that John warns of an entity coming in its "purest form" with bloody tendrils. The orb attacks Sensei with tendrils.
This might also be related to the mighty sky tendrils that Yasu talked about when Makoto's dad died.
Yasu was prewarned of that event by hearing the whispers of the world itself, something she's heard on many occasions. Sensei hears whispers coming from the orb.
The four orbs of power that make up the orb are plant, worm, fist, and red. These could be random, but if we try to match them to the trinity: in Life of Prizes a worm crawls out of the Lust Eater's book (USER1), Wires is regularly connected to growing plants (and they're both green), and Pareidolia's color is red. So fist might represent USER4 - I can't think of any implications there, but maybe someone else can come up with something.
I've got some more thoughts on the orb coming in a tinfoil theory I'm working on, so stay tuned.