Open files are the natural home of the rooks. Seizing one — often by doubling both rooks on it — lets you invade the opponent's camp, attack backward pawns, and trade off the defender's rooks on your terms. The struggle to control the only open file is a defining theme of many middlegames.
A file is 'half-open' for you if only the opponent has a pawn on it; these are excellent files to attack along, since your rook pressures that pawn directly. Planning your rook placement around current and future open files is one of the clearest, most practical strategic skills.