I guess this has to do with identity. The essence of identity is the set of qualities that the identity requires (is necessary) to set itself apart (as unique) from the rest.

Essence, in the interpretation above, is illusory because we all share qualities with the not-self either in part or as a whole. A twin shares his father's looks in part and his twin's in whole. Where is that complete and separate essence that defines the twin in question? It's nonexistent.

That said, the ''normal'' is that we do assign identity - selfness - to entities and that means an ''essence'' has been captured at some level.

I would be surprised to hear that Hume had written anything about Essence. Hume was an empiricist and a sceptic and believing in essences requires a metaphysical, rationalist approach - almost the opposite of Hume's worldview.

I'd say that everything could be described as a bundle of properties.

Re essence, it's simply an individual's criteria to apply an abstraction or concept. In other words, it's what an individual requires to call some x (some particular) an F (some universal/abstract/concept term).