Deep Structure (D-Structure) is is one of the early elements of Noam Chomsky's transformational generative grammar theory (TGG). Its complement is Surface Structure (S-Structure). It is important to note that Deep Structure and Surface Structure were supplanted by Logical Form (LF) and Phonetic Form (PF) in the 1990s versions of Chomsky’s theory, which are themselves supplanted by economy of derivation and economy of representation in Chomsky's latest Minimalist program theory.
D-Structure relates to the effort to identify the universal grammar: the grammatical principles that underlie, at a deep innate level, the grammars of all languages, each of which is performed at a surface communication level. D-Structure is then the deep innate and universal principles of grammar upon which all languages depend, despite the vast surface differences between languages, for example, the surface differences between Japanese and English; deep structure universal grammatical principles are transformed to generate correct grammatical structures at the surface level of any given language.
With the emergence of Chomsky's Minimalist program, Chomsky is still clear that deep knowledge underlying the human ability to speak and understand is innate. This means that at a deep level, prior to culture or language, babies have prior knowledge of the universal structure of language upon which the surface knowledge of the phonetical and grammatical knowledge of a given language will be superimposed.
Chomsky was eventually led to claim that these sentences have several different syntactical structures, that the uniform surface structure of, e.g., "I like her cooking" conceals several different underlying structures which he called "deep" structures. The introduction of the notion of the deep structure of sentences, not always visible in the surface structure, is a crucial element of the Chomsky revolution, (John R. Searle, 1972).