Non-rigid designators are expressions that do not refer to the same object in every possible context; their reference can vary depending on the situation or the conditions in which they are used. Unlike rigid designators, which refer to the same entity across all possible worlds, non-rigid designators can change their reference based on context or the attributes being ascribed. This quality plays a crucial role in discussions about proper names and definite descriptions, where the meaning and reference of terms may shift depending on how they are employed in various contexts.