There is a possible as opposed to the impossible, and a possible as opposed to the necessary (God and energy are possible beings in the first sense, but not in the second). A “possible world” is clearly concerns a possibility as opposed to impossibility, and therefore it formally consists in all that is such that it is not necessary that it not exist.
To establish this kind of possibility can require three things:
1.) Establishing it absolutely. The most common kind of such “possibility” is when “possible” (or its negation or a synonym) is in the subject of a statement “the possible can either be or not be” or “impossibility of existence is denied of the contingent”. There is an abstraction from The concrete, existent world (whether actual or possible).
2.) Establishing it on the side of the matter. Why can’t I make a pterodactyl omelets? Because the stuff to make them out of doesn’t exist. They are impossible.
3.) Establishing it on the side of the agent. Why can’t I hear Mozart improvise or watch Michelangelo sculpt? We have even better pianos and chisels than either of them had access to, and the air vibrates just as well know as it did in 18th century Salzburg. There is no impossibility on the side of the matter, but the absence of an agent makes these impossible.
Notice that the latter two kinds of possibility are determined by some kind of natural inquiry, even if it is a pretty minimal natural inquiry. This kind of possibility is immediately reduced to some sort of appeal to sensation. The first kind of possibility is not immediately reduced in this way, and so has a kind of independence from natural science. A physicist is not the person you would go to in order to figure out, say, the sort of discussion of possibility we are having now- a discussion of the divisions and distinctions in the very subject of possibility.