A concept popularized in academic circles by Noam Chomsky in his book Syntactic Structures (published in 1957), then in geek circles by Neal Stephenson in his novel Snow Crash (published in 1992). The basic idea is that grammar consists of "surface structures", which are the words and/or sounds in a sentence and "deep structures", which contain the meaning of the sentence. The deep structures are converted to surface structures by a ordered set of rules.
Chomsky's theory was that the deep structures of the brain are inborn, meaning children have a natural capacity for language that is acquired rather then learned. One implication of this is that there is a biological limit to the variety of language humans will develop and understand. Another is that the same concept in two different languages would have the same deep structure, but different surface structures; learning new languages does not change the way you think or what you think about, though learning new concepts does.
The theory Stephenson presented was rather that the deep structures resemble the machine code in a computer; they define how we respond to language, but can be altered themselves by language. Hence learning a new language can change the way you think. He even suggests that (SPOILER ALERT!) it might be possible to hack into people's minds by accessing their deep structures (END SPOILER).
In neurological circles, the term refers to the inner structures of the brain, such as the thalamus, basal ganglia, pons, and cerebellum.