Getting a grasp on this idea feels like trying to pin down a cloud.
Big U-niverse = Universe (includes all the multiverses, true totality of everything & all potential, All That Is & Isn't)
Little u-niverse = universe (includes only this time-space reality, like C-137 baryonic matter reality)
The universe (aka 'Little u-niverse') is necessarily a subset of the Universe (aka 'Big U-niverse'), which is essentially the universal set (or universal class, to avoid Russel's paradox). The Universe is essentially an endless multiverse each composed of endless multiverses themselves, but the universe is just the parts of the Universe that WE have access to in the here & now, which is incredibly small compared to All That Is & Isn't (which together make up the Universe).
All That Is, is much easier for most people to imagine, than All That Isn't. I'm unsure if we will ever find empirical evidence to support the non-existence of All That Isn't, since it is necessarily a part of the Universe we would never be able to reach while we exist in our human form. Maybe it doesn't even exist at all (yes, I see the irony), and the whole concept is crazy. But, I shrug, and remind people that life is often stranger than fiction, and the world is composed of interplay of opposites.
Even though we can conceive of "All That Is" but cannot really conceive of "All That Isn't", it is important to make this distinction because in both domains there is much that we still do not know. We know much less of All That Isn't than we know of All That Is, and we don't know that much of All That Is at all. We have barely scratched the surface of knowledge, even though capitalism would like us to think that everything that can be known is already in economic circulation. The truth of our universe and indeed the Universe at large is far greater than any conception humans have come up with thus far. Our own universe cannot be contained by dogma, much less the Universe at large.
The scientific method can currently only function within the Little u-niverse because we currently have no way to reap information from other dimensions besides our own time-space reality. The closest we have come to understanding the Big U-niverse is in our knowledge of black holes, where space and time as we know it disintegrates into meaninglessness. Scientists balk at the very idea of meaninglessness, because science is supposed to establish meaning. I, on the other hand, enthusiastically embrace nihilism, and I'm not afraid to intellectually tread in places where some scientists will not dare go, so I'll pick up where science leaves off.
In the storyline of The Fantastic Universe Of Anjie Zealand video game I'm currently creating, 'Big U-niverse' and 'Little u-niverse' is how the main characters distinguish between the universe/world that's local to them as opposed to the Universe at large that composes all of the universes/worlds. Ironically, this isn't just a science fiction plot device I'm using— it's really how I think the real world likely works.