It's important to note that David Lewis doesn't have a monopoly on the use of the term
possible world and I think some of the answers above are confusing modal logic itself with some much more controversial metaphysical views.
As far as the standard Kripke semantics for modal logic are concerned, a
possible world is a just a set of assignments of truth-values (T or F) to a set of atomic formulae. Therefore, as far as the semantic theory of modal logic is concerned,
possible worlds are abstract objects like a numbers or sets.
Call the thing that we live in, right now, in which Barack Obama is the current U.S. president and so on
the universe. Now, you might think that
the actual world must be one of the possible worlds, and so at least the actual world must be one concrete possible world. Again, this would be wrong.
The actual world is just an abstract object too--it is the world which assigns all the atomic formulae the truth values that obtain in the universe. So the universe =/=
the actual world.
modal realism involves the claim that each of the possible worlds (not just the actual world) has some universe that makes it true. These other universes are supposed to be the concrete things. Lewis has interesting metaphysical argument for why this must be the case, but it is clear that this is a strictly metaphysical argument. The claim doesn't follow from the semantics of modal logic itself.
Now Lewis might be right about
modal realism or he might be wrong. Perhaps it is the case that possible worlds interpretations of QM give some evidence in favor of Lewis's modal realism or it might not. But it is very important to note that what
possible worlds are supposed to be in this interpretation of QM are what we were calling above "other universes", that is, they are concrete objects, not just abstract sets of assignments of truth values. I don't have the expertise to weigh in on the evidence for or against this view of QM: I just want to make clear exactly what role such evidence would play in the philosophical dispute at issue here.