After reading David Oderberg's book Real Essentialism I've been concerned with getting a clear understanding of what "essences" are. Essences are not substances in themselves, over and above the entities which have them. On the other hand, they are supposed to provide explanatory power for the objects that have them, and they are supposed to have a specific sort of causal importance, in Aristotle's terms what is called "formal causation". In trying to make sense of these notions I have found truthmaking to be somewhat helpful (provided of course we have a good account of truthmaking). Here's an analysis:
Essence: For any entity X the essence of X is the truthmaker of the proposition that the real definition of X is [such and such].
To begin with, let's be clear about what exactly a truthmaker is. A truthmaker is some fact or aspect of reality in virtue of which a truthbearer, such as a proposition, statement, belief, etc., is true. How exactly is truthmaking helpful here? Well, it describes a real aspect of a thing.
Kit Fine provides a popular neo-Aristotelian definitional account of essences, saying that we can give real definitions of not only words, but entities, in order to explain what they are. These real definitions of objects are their essences. More work needs to be done on getting to the heart of what real definitions are and how we come to know them. (A possible account of what they are, which I am now somewhat doubtful of, is here.) But provided we have a clear understanding of this, Fine's account certainly seems to be on the right track, especially in the face of the failure of some modalist accounts. But according to the classical account, essences not only make things to be what they are; they provide explanations for causal powers. Definitions, which are linguistic entities, obviously do not.
As Kathrin Koslicki puts it in her paper "Essence, Necessity, and Explanation", "A definition, according to Aristotle, is a formula or statement of the essence, i.e. of what it is to be a certain kind of thing." She continues, "On Aristotle’s way of thinking, then, the explanatory power inherent in definitions, in their role as the linguistic correlates of essences, is a direct reflection of the causal power of essences." Since real definitions are the linguistic correlates of essences, truthmaking provides a way to get back to the essence itself.