"that roars or bellows; making or characterized by noise or disturbance," late 14c., present-participle adjective from roar (v.). Used of periods of years characterized by noisy revelry, especially roaring twenties (1930, which OED credits to "postwar buoyancy"); but also, in Australia, roaring fifties (1892, in reference to the New South Wales gold rush of 1851). Roaring Forties in reference to exceptionally rough seas between latitudes 40 and 50 south, is attested from 1841.
The "roaring fifties" are still remembered as the days when Australia held a prosperity never equalled in the world's history and a touch of romance as well. The gold fever never passed away from the land. [E.C. Buley, "Australian Life in Town and Country," 1905]
Roaring boys, roaring lads, swaggerers : ruffians : slang names applied, about the beginning of the seventeenth century, to the noisy, riotous roisterers who infested the taverns and the streets of London, and, in general, acted the part of the Mohocks of a century later. Roaring girls are also alluded to by the old dramatists, though much less frequently. [Century Dictionary]
This is from the use of roar (v.) in old London slang for "behave in a riotous and bullying manner" (1580s).