To run interference means to provide assistance by or as if by clearing a path through obstructions. In football, it describes the effort of the offensive players to block the defensive players from reaching the player in possession of the ball.
The idiom came into use first in football, in the early 1890s. By the middle of the 20th century it had broadened to include non-sporting use.
Noah Gerber has played tackle in several hard games and ranks as first sub after Deardorf’s place. He weighs 160, is good at making holes, and holds his place splendidly in running interference.
— The Indianapolis Journal (Indianapolis, IN), 29 Nov. 1893
Director James F. Byrnes of the Office of Economic Stabilization probably will “run interference” for a new tax measure—expected to include some form of compulsory savings—in congress next year, authoritative administration sources said today.
— Chicago Tribune, 19 Nov. 1942