Deep structure and surface structure

The original idea of Chomksy's "Deep Structure"was that multiple "surface forms" are often used to express the same concept. The classic example was the passive construction; e.g., "John loves Mary" supposedly expresses the same idea as "Mary is loved by John". These two "surface structures" were said to be derived from the same deep structure ("John loves Mary") by "transformations", which is why the theory came to be called "transformational grammar".

Unfortunately, the "surface" appeal of the Deep Structure concept soon led people from unrelated fields (architecture, music, politics) to misuse and abuse the term to express various things in their own work, which rarely if ever had the mathematical rigor of Chomsky's linguistic scholarship. It was perhaps this situation that led Chomsky and his students to abandon the term entirely, replacing it with the supposedly meaningless abbreviation "DS", and eventually abandoning the deep/surface distinction, as well as transformations, altogether.

Current Chomskyan linguistics focuses instead on relating various representations (meaning, structure, sound) to each other in a way that doesn't make any of them deep or fundamental. Hence, one way to make yourself look pretentious, misinformed, and tragically unhip to a group of linguists is to say something about the "Deep Structure" of the mind, supposedly revealed by Chomsky. To be fair, this is more a matter of nomenclature than anything else, as the most robust (and controversial) notion put forth by Chomsky has been the concept of a "Universal Grammar" that constrains the overall forms of linguistic expression available to the human species. This concept -- more of a grammar-schema than a grammar -- is probably what non-linguists are referring to when they say "Deep Structure".

Reference:

Chomsky, N. (1957/2002) Syntactic Strucutres. DeGruyter.