late 14c., "land under the jurisdiction of a town, state, etc.," probably from Latin territorium "land around a town, domain, district," from terra "earth, land" (from PIE root *ters- "to dry") + -orium, suffix denoting place (see -ory). Sense of "any tract of land, district, region" is first attested c. 1600. Specific U.S. sense of "organized self-governing region not yet a state" is from 1799. Of regions defended by animals from 1774.
"Since -torium is a productive suffix only after verbal stems, the rise of terri-torium is unexplained" [Michiel de Vaan, "Etymological Dictionary of Latin and the other Italic Languages"]. An alternative theory, somewhat supported by the vowels of the original Latin word, suggests derivation from terrere "to frighten" (see terrible); thus territorium would mean "a place from which people are warned off."