To read structure out of a sequence. Parsing decides where the parts begin and end, and that decision can be wrong.
Latin pars orationis, literally 'part of speech', from pars (a part); to parse first meant naming the grammatical role of each word in a sentence, before it meant reading structure out of any sequence.
To read structure out of a sequence, deciding where its parts begin and end — a decision the house treats as fallible, because it can be wrong.