Full Idea
When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed.
Gist of Idea
An essential property is true of an object in any case where it would have existed
Source
Saul A. Kripke (Naming and Necessity lectures [1970], Lecture 1)
Book Reference
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.48
A Reaction
This seems to equate essence with necessary properties, which is the view attacked nicely be Fine in 1994. I take essence (in Aristotle's sense) to be quite different from necessary properties (in being non-trivial, for example).