To take a firm position. The analogy presumably is to setting one or both feet in a fixed position, representing a firm stand. Although versions of this term (usually with set one’s foot down) exist from the sixteenth century on, it became current only in the nineteenth century. The OED cites James Payn’s The Luck of the Darrells (1886): “She put her foot down . . . upon the least symptoms of an unpleasantry.”