As far as I understand it, in modern philosophy the point of the notion of possible worlds is around in order to make sense of reference based semantics.
The idea of reference-based semantics is that meaning boils down to reference, -- the meaning of dog is everything that is (correctly) referred to by "dog" and the meaning of a proposition is its truth conditions.
This idea runs into problems when you consider some word like "unicorn" which refers to nothing in this world, and yet doesn't mean nothing, nor does it mean the same as centaur which also refers to nothing in this world, -- so philosophers save reference-based semantics by arguing that it refers to unicorns in some possible world. More or less.
I don't know that I buy it really, because in general reference-based semantics seems to presuppose some kind of realism that I find unconvincing.
As far as I know the philosophical construct of possible worlds doesn't have a lot to do with possible worlds as in the movie above. Though I must say I find the idea of God rewinding to edit random events, slightly far-fetched. If there are multiple realities I guess they only arise at significant choice points.