It comes to English from French, where it traces back to a Middle French word meaning "to prepare." And the original English-language parades did indeed require preparation. When the English started using the word parade in the mid-1600s it referred—as it did and does in French—to a pompous show, an exhibition.

Etymology Noun borrowed from French, "show, display (of an object to demonstrate its value), show of military force, cavalry procession," going back to Middle French, from parer "to prepare, adorn, dress (a person) with care" (going back to Old French) + -ade -ade — more at pare

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").

Originally the processions were religious. But their form has survived for centuries, easily metamorphosing from religious processions into royal entries, popular festivals, and, since the beginning of the twentieth century, commercial events such as the American parade.