late 14c., in reference to the large, oblong, unroofed enclosures used for races, etc., in ancient Rome, from Latin circus "ring, circular line," which was applied by Romans to circular arenas for performances and contests and oval courses for racing (especially the Circus Maximus), from or cognate with Greek kirkos "a circle, a ring," perhaps from PIE *kikro-, reduplicated form of root *sker- (2) "to turn, bend." The adjective form is circensian.
In reference to modern large arenas for performances of feats of horsemanship, acrobatics, etc., from 1791, sense then extended to the performing company itself and the entertainment given, hence "traveling show" (originally traveling circus, 1838). Extended in World War I to squadrons of military aircraft. Meaning "lively uproar, chaotic hubbub" is from 1869.
Sense in Picadilly Circus and other place names is from early 18c. sense "buildings arranged in a ring," also "circular road."