department (n.) Look up department at Dictionary.com
mid-15c., "a going away, act of leaving," from Old French departement (12c.) "division, sharing out; divorce, parting," from Late Latin departire "to divide" (transitive), from de- "from" (see de-) + partire "to part, divide," from pars (genitive partis) "a part, piece, a share, a division" (from PIE root *pere- (2) "to grant, allot").

French department meant "group of people" (as well as "departure"), from which English borrowed the sense of "separate division, separate business assigned to someone in a larger organization" (c. 1735). Meaning "separate division of a government" is from 1769. As an administrative district in France, from 1792.