Full Idea
The 'explanatory characterization' says that the essential properties of an object are the object's deepest explanatory properties, which explain the other properties of the object - and which Copi claims is mind-independent.
Gist of Idea
Essential properties are the 'deepest' ones which explain the others
Source
report of Irving M. Copi (Essence and Accident [1954]) by Adolph Rami - Essential vs Accidental Properties §2
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.6
A Reaction
It is, of course, normal to see a good explanation as being dependent on the interests of the audience. Perhaps this account should be in terms of causal powers. See Shoemaker on properties.