According to Wikipedia, "any definition that attempts to set out the essence of"
I haven't looked at the wikipedia article, but the view it expresses is VERY old-fashioned. Since Wittgenstein's "family resemblance" concept, and especially since cognitive scientists such as Eleanor Rosch's work in the 1970s, it's far more fashionable to think of concepts (and categories) as constituted not by "necessary and sufficient conditions" but by prototypes and similarity relations, far more befitting "fuzzier" concepts -- for example the way we think about "dogs" is not to generate an "essence" of necy/sufficient conditions, but by having in mind some prototypical dog at the center and then linking it to less familiar, less central, other examples ... This is far more in keeping with your nice suggestion, that what we seek (as I'd put it) are some "characteristic" properties of the paradigmatic members of the set, recognizing that other creatures may share these properties to various degrees and still count as members of the set in question ... So unless the wikipedia article was specifically using the word "essence" to mean what it used to mean (necy/suffic condns), and to distinguish essences from concepts, then I'd say your view is far more on the right track than the wiki's view ....
hope that's useful--