Full Idea
The main and the original motivation for the 'possible worlds analysis' - and the way it clarified modal logic - was that it enabled modal logic to be treated by the same set theoretic techniques of model theory used successfully in extensional logic.
Gist of Idea
Possible worlds allowed the application of set-theoretic models to modal logic
Source
Saul A. Kripke (Naming and Necessity preface [1980], p.19 n18)
Book Reference
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.19
A Reaction
So they should be ascribed the same value that we attribute to classical model theory, whatever that is.