How do possible worlds help explain the meaning of necessity?

In the philosophy of logic, the concept of possible worlds provides a framework for defining modal properties, such as necessity, by describing how propositions hold true across different scenarios.1

Under this possible-world semantics, the meaning of necessity is explained through the following criteria:

• Necessity: A proposition is considered necessarily true if and only if it is true in all possible worlds. This contrasts with contingent truths, which are true in the actual world but false in at least one other possible world.213
• Impossibility: A proposition is impossible if it is true in no possible worlds.1
• Possibility: A proposition is possibly true if it is true in at least one possible world.21

This approach also extends to modality de re, which concerns the essential properties of things. An object possesses a property necessarily if it retains that attribute in every possible world in which the object exists. While some philosophers view these worlds as abstract objects, others, such as David Lewis, have defended modal realism, arguing for the concrete existence of a plurality of such worlds.12