Explanatory in this sense refers to the ability of a given linguistic theory to describe how a component of language is acquired by a child (as proposed by Noam Chomsky; see Levels of adequacy).
His starting point is a close analysis of the meanings of lexemes dedicated to bringing out parallelisms and contrasts which reveal the nature of the conceptual structures underlying them.
What his method shows, he says, is that the psychological organization on which meaning rests 'lies a very short distance below the surface of everyday lexical items – and that progress can be made in exploring it' (1991: 44).
Conceptual semantics breaks lexical concepts up into ontological categories: events, states, places, amounts, things, and property, to name a few.
Conceptual semantics is compositional, in that the meanings of phrases, clauses, and sentences can be determined from the lexical concepts that make them up.
(Murphy 2010:66) Jackendoff's system has been criticised for its highly abstract primitives, which linguists such as Wierzbicka (2007a, 2007b) and Goddard (1998, 2001) have called "obscure".
With this proviso, however, I think a particular choice of primitives should be justified on the grounds of its capacity for expressing generalizations and explaining the distribution of the data.