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Full Idea
Some properties of an object may be essential to it, in that it could not have failed to have them. But these properties are not used to identify the object in another possible world, for such an identification is not needed.
Gist of Idea
Identification across possible worlds does not need properties, even essential ones
Source
Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 1)
Book Ref
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.53
A Reaction
So how DO you identify objects in other possible worlds, or in this one? You may say he was baptised 'Aristotle' so that's rigid, but if Athens is full of pseudo-Aristotles I want to pick out the real one. I say Kripke muddles epistemology and ontology.