Perhaps the English word originally is from a derivative of Old French garbe/jarbe "sheaf of wheat, bundle of sheaves," though the sense connection is difficult. This word is from Proto-Germanic *garba- (source also of Dutch garf, German garbe "sheaf"), from PIE *ghrebh- (1) "to seize, reach" (see grab (v.)).
"In modern American usage garbage is generally restricted to mean kitchen and vegetable wastes" [Craigie]. Used figuratively for "worthless, offensive stuff" from 1590s. Garbage can is from 1901. Garbage collector "trash man" is from 1872; Australian shortening garbo attested from 1953. Garbology "study of waste as a social science" is by 1976; garbologist is from 1965.
1848, "practical and scientific methods of preservation of health and promotion of sanitary conditions," irregularly formed from sanitary. The somewhat euphemistic use in reference to garbage and domestic waste disposal is (as in sanitation engineer) is by 1916 (sanitation man).
late 14c., "thing of little use or value, waste, refuse, dross," perhaps from a Scandinavian source (compare Old Norse tros "rubbish, fallen leaves and twigs," Norwegian dialectal trask "lumber, trash, baggage," Swedish trasa "rags, tatters"), of unknown origin. Applied to ill-bred persons or groups from 1604 ("Othello"), and especially of poor whites in the U.S. South by 1831. Applied to domestic refuse or garbage from 1906 (American English). Trash-can is attested from 1914. To trash-talk someone or something is by 1989.