Thank you for the question, Bone cruncher. Yes, I do mean the deconstruction of sentences as you noted -- although I abhor the the word 'deconstruction', preferring, perhaps, the word 'analysis'. It is a visual tool which may be used to analyze a sentence, which was popular in America for about 75 - 100 years, until the 1960s or 1970s (I, myself, encountered the exercise in the 1950s.) I do not know your age or where you live, so you may not have had the pleasure(?) of diagramming sentences.
It is a good tool for writers, who strive for clarity in constructing coherent, complex sentences. It is not something one consciously should do all the time--lord knows nothing would get written if it were!--but it is something a writer should be aware of to get his/her ideas to the reader as intended.
I cannot use HTML or other tools to illustrate a diagrammed sentence. However, if you Google 'diagramming sentences' you will find many sites which illustrate this lost art.