Transformational-generative grammar is a system of language analysis that recognizes the relationship among the various elements of a sentence and among the possible sentences of a language and uses processes or rules (some of which are called transformations) to express these relationships. For example, transformational grammar relates the active sentence "John read the book" with its corresponding passive, "The book was read by John." The statement "George saw Mary" is related to the corresponding questions, "Whom [or who] did George see?" and "Who saw Mary?" Although sets such as these active and passive sentences appear to be very different on the surface (i.e., in such things as word order), a transformational grammar tries to show that in the "underlying structure" (i.e., in their deeper relations to one another), the sentences are very similar. Transformational grammar assigns a "deep structure" and a "surface structure" to show the relationship of such sentences. Thus, "I know a man who flies planes" can be considered the surface form of a deep structure approximately like "I know a man. The man flies airplanes." The notion of deep structure can be especially helpful in explaining ambiguous utterances; e.g., "Flying airplanes can be dangerous" may have a deep structure, or meaning, like "Airplanes can be dangerous when they fly" or "To fly airplanes can be dangerous." www.Britannica.com.

There isn't really any way to explain this in plain language, it is kind of complicated. Basically it is the idea that each sentence in a language has two levels of representation — a deep structure and a surface structure. The deep structure represents the core semantic relations of a sentence, and is mapped on to the surface structure via transformations. There are considerable similarities between languages' deep structures, and these structures reveal properties, common to all languages, which are concealed by their surface structures. If you say something in Russian or English or Chinese, the deep meaning of the sentence is the same and the components of the sentence at the deepest level can be compared. I am not sure that I fully understand the concept but I did my best.