Full Idea
Aristotle calls a substance a nature. This expresses essence as what underlies a thing's characteristic behaviour, whereas whatness expresses it as underlying the definition, and essence refers to it as that through which and in which it has existence.
Gist of Idea
Aristotelian essence underlies behaviour, or underlies definition, or is the source of existence
Source
report of Aristotle (Metaphysics [c.324 BCE]) by Thomas Aquinas - De Ente et Essentia (Being and Essence) p.92
Book Reference
Aquinas,Thomas: 'Selected Philosophical Writings', ed/tr. McDermott,Timothy [OUP 1993], p.92
A Reaction
I don't really understand the third one, unless it is what gives something its identity, which probably then reduces to the second one. The big choice is between essence explaining behaviour and essence explaining definition. Interesting.