Full Idea
Socrates has P essentially if he has P in every world, or has it in every world in which he exists, or - most plausible of all - has P in the actual world and has its complement [non-P] in no world.
Gist of Idea
X is essentially P if it is P in every world, or in every X-world, or in the actual world (and not ¬P elsewhere)
Source
Alvin Plantinga (World and Essence [1970], Intro)
Book Reference
Plantinga,Alvin: 'Essays in the Metaphysics of Modality' [OUP 2003], p.49
A Reaction
These strike me as mere necessary properties, which are not the same thing at all. Essences give rise to the other properties, but Plantinga offers nothing to do the job (and especially not 'Socrateity'!). Essences must explain, say I!