Full Idea
An individual essence is a profile that is necessary and sufficient for some particular thing.
Gist of Idea
An individual essence is a necessary and sufficient profile for a thing
Source
John Hawthorne (Causal Structuralism [2001], Intro)
Book Reference
Hawthorne,John: 'Metaphysical Essays' [OUP 2002], p.212
A Reaction
By 'for' he presumably means for the thing to have an existence and a distinct identity. If it retained its identity, but didn't function any more, would that be loss of essence?