late 14c., demonstracioun, "proof that something is true," by reasoning or logical deduction or practical experiment, from Old French demonstration (14c.) and directly from Latin demonstrationem (nominative demonstratio), noun of action from past-participle stem of demonstrare "to point out, indicate, demonstrate," figuratively, "to prove, establish," from de- "entirely" (see de-) + monstrare "to point out, show," from monstrum "divine omen, wonder" (see monster).
Sense of "exhibition and explanation of practical operations" is by 1807. Meaning "public show of feeling by a number of persons in support of some political or social cause," at first usually involving a mass meeting and a procession, is from 1839. Related: Demonstrational.