Very roughly, you might think of a possible world as a complete description of the way things might have been, including a complete description of the farthest future as well as the farthest past.  More precisely, a possible world W is maximal in this sense: For any state of affairs S, W will include either S or its complement non-S.  That, no doubt, is something of a mouthful, and may not communicate a lot.  But just think of a possible world in terms of completeness.  A given possible world will include either the fact that unicorns exist or the fact that they do not, either the fact that Lincoln was assassinated in 1865 or the fact of its not being the case that Lincoln was assassinated in 1865, either the fact that God created the heavens and the earth or the fact of its not being the case that God created the heavens and the earth.

    Now one very obvious example of a possible world is the actual world, the one in which you and I exist and in which we are now interacting at least to the extent that you are now reading these words.  But keep in mind that the actual world includes more than the earth, more than our solar system, more than our galaxy, and even more than the universe itself (if you think of there being more than one universe or several universes existing in different dimensions).  For the actual world includes everything that exists.  You might think of it as being just what the set of true propositions describes.

    So is there more than one possible world?  If you accept the idea of contingency, the idea that some things could have been different, then you must also accept the idea of other possible worlds--of other ways that things might have been.  If it is logically possible, for example, that my beloved dog might not have died in June, 1997 (he was finally euthanized to put him out of his misery), then there is another possible world--another way things might have been--in which he does not die in June, 1997.  This other way things might have been may be very similar to the actual world up until June, 1997, but it will diverge from the actual world at this time because in this other world my dog continues to survive.  This, of course, is of no psychological comfort to me, since this other possible world in which my dog continues to survive is not the actual world.  But fortunately, I also believe in immortality for animals (at least for the higher mammals, if not for mosquitoes and fleas) no less than I do for human beings.