"refuse, filth," 1580s; earlier "giblets, refuse of a fowl, waste parts of an animal (head, feet, etc.) used for human food" (early 15c., in early use also gabage, garbish, garbidge ), of unknown origin; OED says probably from Anglo-French "like many other words found in early cookery books." In its sense of "waste material, refuse" it has been influenced by and partly confused with garble (q.v.) in its older sense of "remove refuse material from spices;" Middle English had the derived noun garbelage but it is attested only as the action of removing the refuse, not the material itself.
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.