There are at least three major different uses of "multiverse". The way it's described above is the familiar one from
science fiction.
The word was coined by the pragmatist philosopher William James in 1895, and included in his 1897 collection Will to Believe: "Visible nature is all plasticity and indifference, -- a moral multiverse, as one might call it, and not a moral universe."
He was not talking about multiple universes. The original quote is not very clear, but he used it again in "The One and the Many", lecture 4 in Pragmatism (1907):
'The world is one,' therefore, just so far as we experience it to be concatenated, one by as many definite conjunctions as appear. But then also not one by just as many definite disjunctions as we find. The oneness and the manyness of it thus obtain in respects which can be separately named. It is neither a universe pure and simple nor a multiverse pure and simple. And its various manners of being one suggest, for their accurate ascertainment, so many distinct Programs of scientific work. Thus the pragmatic question 'What is the oneness known-as? What practical difference will it make?' saves us from all feverish excitement over it as a principle of sublimity and carries us forward into the stream of experience with a cool head. The stream may indeed reveal far more connexion and union than we now suspect, but we are not entitled on pragmatic principles to claim absolute oneness in any respect in advance.
Well okay, that's not entirely clear either. What he's arguing
against is
mystical statements of the kind "all is one", or "all things are connected": far from embodying some sublime
insight, they are empty waffle.
When a young man first conceives the notion that the whole world forms one great fact, with all its parts moving abreast, as it were, and interlocked, he feels as if he were enjoying a great insight, and looks superciliously on all who still fall short of this sublime conception. Taken thus abstractly as it first comes to one, the monistic insight is so vague as hardly to seem worth defending intellectually. Yet probably everyone in this audience in some way cherishes it. A certain abstract monism, a certain emotional response to the character of oneness, as if it were a feature of the world not coordinate with its manyness, but vastly more excellent and eminent, is so prevalent in educated circles that we might almost
call it a part of philosophic common sense. Of course the world is one, we say. How else could it be a world at all? Empiricists as a rule, are as stout monists of this
abstract kind as rationalists are.
The difference is that the empiricists are less dazzled. Unity doesn't blind them to everything else, doesn't quench their curiosity for special facts, whereas there is a kind of rationalist who is sure to interpret abstract unity mystically and to forget everything else, to treat it as a principle; to admire and worship it; and thereupon to come to a full stop intellectually.
The sense is really that the universe is not a unity. He is still talking about "the universe", however. The next shift of meaning was that it is not a cosmos, an ordered construction: the physicist Sir Oliver Lodge (who was also interested in the paranormal, which I think can be taken into account here) said in 1904 that the "only possible alternative was to regard the universe as a result of random chance and capricious disorder, not a cosmos or universe at all, but rather a 'multiverse'."
And so on: the OED quotes Sir Cyril Burt, as late as 1975, in much the same sense, and hasn't noticed the science-fiction sense at all yet: "Modern physics presents us with a heterogeneous multiverse, in place of the homogeneous universe of Newton and Laplace."
The second major sense is the one explored in the write-ups above: a collection of different universes, a group of them, each one of which looks something like our own, and of which our own is one. They may very well be interconnected and can be visited or moved between. Note that this makes no sense in James's use. He was talking about a way of seeing the one universe: seeing it as many-faceted, with different relationships and connexions running through it.
But the science-fiction sense says there are multiple universes within the multiverse, as there may be multiple planets in a galaxy, or rooms in a house.
There are at least two entirely different ways such a scenario is possible in orthodox (though speculative) science. First, in the Era of Inflation, the Big Bang universe expanded faster than the speed of light, meaning that different regions from what was once a single ultra-hot ultra-dense universe have now separated from each other and are permanently beyond each other's observable horizon. They are effectively island universes.
Another possibility is that the Big Bang did not happen once but happens arbitrarily often in certain conditions: huge chance fluctuations in the quantum vacuum, or inside a black hole, or reversing a Big Crunch at the end of time. Each of these produces a region of spacetime inaccessible from "outside", even though there is more to existence than just that region.
Both these possible mechanisms allow for (but do not I think require) physical constants to be different in each region of the multiverse, so you can have different fundamental behaviour of reality.
Also, both might (might) allow interconnexion via arcane forms of travel (a "wormhole" or whatever, details not important here), overcoming the inaccessibility through normal space.
David Deutsch in his The Fabric of Reality uses the term differently again: unfortunate, I think, because the second sense is pretty well established. He doesn't think there are other kinds of place. His is getting closer to the Jamesian original. He says that there is not one single universe which is real (and other possible ones aren't), but rather that all possible universes are simultaneously real. It is a kind of illusion, an anthropic illusion, that any observer seems to be observing a single real fabric of events and things: a universe. In fact every such universe is neither more nor less privileged than any other, and the set of all allowable quantum states is the multiverse.