mid-14c., discussioun, "examination, investigation, judicial trial," from Old French discussion "discussion, examination, investigation, legal trial" and directly from Medieval Latin discussionem (nominative discussio) "examination, discussion," in classical Latin, "a shaking," noun of action from past-participle stem of discutere "strike asunder, break up," in Late Latin and Medieval Latin also "to discuss, examine, investigate," from dis- "apart" (see dis-) + quatere "to shake" (see quash).
Meaning "a talking over, debating" in English first recorded mid-15c. Sense evolution in Latin appears to have been from "smash apart" to "scatter, disperse," then in post-classical times (via the mental process involved) to "investigate, examine," then to "debate."