late 15c., "an appeal, request," a sense now obsolete, from Old French remonstrance (15c., Modern French remontrance), from Medieval Latin remonstrantia, from present-participle stem of remonstrare "point out, show," from re-, here perhaps an intensive prefix (see re-), + Latin monstrare "to show" (see monster).
The sense of "a strong formal representation of reasons or statement of facts against something complained of or opposed" is from 1620s. Also in history with specific political and ecclesiastical senses. Related: Remonstrant (n., adj.).