c. 1500, "a command, a judicial or legal order," from French mandat (15c.) and directly from Latin mandatum "commission, command, order," noun use of neuter past participle of mandare "to order, commit to one's charge," literally "to give into one's hand," probably from manus "hand" (from PIE root *man- (2) "hand") + dare "to give" (from PIE root *do- "to give").
Political sense of "approval supposedly conferred by voters to the policies or slogans advocated by winners of an election" is from 1796. League of Nations sense "commission issued by the League authorizing a selected power to administer and develop a territory for a specified purpose" (also used of the territory so specified) is from 1919.
1620s, "to command," from mandate (n.). Meaning "to delegate authority, permit to act on behalf of a group" is from 1958; used earlier in the context of the League of Nations, "to authorize a power to control a certain territory for some specified purpose" (1919). Related: Mandated; mandating.