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I've just seen a documentary about the multiverse. This provides an explanation for where the big bang came from. But it leaves me wondering: how did the multiverse come into existence?

Because this is a step further than something we don't even surely know the existence of, I'm only wondering if there are any theories or suggestions.

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Which popularization did you see? It is hard to guess what you are talking about. –  Ron Maimon Apr 15 '12 at 7:19
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It is wrong to ask questions which are not logically positivistically meaningful, meaning questions which cannot be reduced to observations of our senses. The "multiverse" concept you encountered is likely one of the following:

  • Large extra dimensions banging branes: This is a physics hoax--- this type of model doesn't work, both because large extra dimensions are ruled out, and because banging branes don't make a big bang.
  • Everett's multiverse: this is the idea that the quantum universe contains branches which we have no experience of, because the quantum universe is so big.

The second type of multiverse is not the same as the first, but it is also difficult to give logical positive meaning to the "existence" of alternate branches that are different from the observed branch. Inasmuch as it is impossible to do experiments on those things, you can assume they are there, or that they are not, however suits your philosophical fancy. Since there is no observational consequence, there is no point in saying anything at all, since the question is not meaningful, but an abuse of language in the sense of Carnap.

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