1650s, "a show of bravado," also "an orderly assembly of troops for inspections," from French parade "display, show, military parade," formerly also "a halt on horseback" (15c.), or from Italian parate "a warding or defending, a garish setting forth," or Spanish parada "a staying or stopping; a parade," all from Vulgar Latin *parata, from Latin parare "arrange, prepare, adorn" (from PIE root *pere- (1) "to produce, procure").
The Latin word developed widespread senses in Medieval Latin: "to stop, halt; prevent, guard against; dress, trim, adorn." These were passed on to its Romanic offspring. The verb is a doublet of parry. Non-military sense of "public walk, march, procession" is recorded from 1670s. Parade-ground is by 1724; parade-rest is by 1888:
[A] position of rest in which the soldier stands silent and motionless, but which is less fatiguing than the position of "attention": it is much used during parades. [Century Dictionary]