"Nazukasokotsune [名塚底根] - the place where all witches begin.”
I've been wanting to talk about this ever since @kcflowers brought it up last year, but it ended up on the back burner until now. I had originally assumed that this name was going to be an easter egg or tidbit that was only decipherable in the production notes, but it turns out to be a major plot point - so important that they had to write it out in text in the trailer in addition to Kyubey's mansplaining. (He's always been a messenger of exposition as well as magic, so of course he'd know all about and be delighted to share his knowledge with us.)
To be honest, I'm not really surprised by this addition- the easiest way to move the story forward after Rebellion is to expand the world and introduce new characters and mechanics, and this is a logical extension of that.
Right now, the existence of "Nazukasokotsune" has been teased, but we don't really know anything about it except for that it's where all witches begin, and the official summary speaks of it in the same breath as Walpurgisnacht and the two new magical girls. The term they use for all three is 存在, "entity" or "existence", which is the broadest and vaguest possible term they could have used.
Some fans are treating it like a person, others like a place, but I suspect it's actually both, similar to how a witch's labyrinth is both a manifestation of a corrupted human soul and a location that others can visit and interact with. This is especially true given the statue at its center, which we can see waking up in this latest trailer. Changes to the rest of the library likely affect the statue and vice versa.
As far as I can tell, this term was made up specifically for the story and doesn't have any other prior usage. However, the individual kanji are suggestive: "name" (名), "burial mound" (塚), "bottom/base/depth" (底) and "root" (根). Thus, it is simultaneously the origin of witches and their tomb, their beginning and their end, the nadir of the cycle. (Recall that circles and cycles are a major theme in this series.) And we see that it is full of books (records) in which witches are named and catalogued - and from which they can emerge.
While the character 塚 can be used to refer to any heap or mound, I've emphasized the "burial" part because I think that's the most relevant meaning in this context. (That said, given some of the shots we've seen of scattered books and pages, I think "heap" will be an accurate description before the end.) The JP Wikipedia page has a long list of different kinds of Japanese mounds, from the kofun (古墳, "old mounds") which are so famous there's an entire era of Japanese history named after them, to various collections of items that serve as monuments and memorials. The one common denominator is that all of them were made by people to serve a distinct (usually commemorative) purpose as opposed to any kind of natural formation.
[Side note: given that most burial mounds (the technical term is "tumulus", btw) end up looking like grassy knolls, you could also make the argument that the green "hill" that is so important to Homura in Rebellion is one. This may or may not be the meaning Inu Curry intended, but once I saw it, it was difficult to unsee.]
Here is where I suspect this is going: the Nazukasokotsune is where the witches collected by the Law of Cycles are "stored" (for the lack of a better term). I also suspect this is its "neutral" state - supported by the fact that the statue has no distinguishing features - and it might look very different if, say, Madokami was restored, or if it was "corrupted" in some fashion.
It's a little confusing, because "Law of Cycles" is used interchangeably to refer to "Madokami" as well as whatever is left once the human Madoka is separate from it. I suspect that part of the reason the term "Nazukasokotsune" was introduced was to help clarify the terms a little better, since otherwise it gets complicated.
In other words, perhaps it's like this:
Madokami/"Law of Cycles" = Madoka + Nazukasokotsune
Walpurgisnacht = Mirror Homura + Nazukasokotsune
It's also possible you could get Walpurgisnacht from a corrupted/damaged Nazukasokotsune, but if Walpurgisnacht is truly the opposite/dark mirror of the Law of Cycles, then it logically should also have a human avatar as well (even if they can still manifest as separate entities similar to what happens in Urobuchi's Godzilla: The Planet Eater film), and there really isn't any other suitable candidate, especially given how many of Walpurgisnacht's motifs Homura's reflection has. They have to be connected in some fashion, even if I haven't gotten the mechanics quite right here.
As I've mentioned before, I think the "Nazukasokotsune" scene we've glimpsed in the trailers is the structural equivalent to the dollhouse scene in Rebellion, in which Kyubey explains what's going on right before all hell breaks loose and the cast fights a giant witch threatening to destroy Mitakihara.