An open file can provide a line of attack for a rook or queen.
Controlling the eighth rank is likely to force the opposing king into a more exposed position and puts pressure on any remaining undeveloped pieces, or if the rank is already clear, allows unobstructed movement behind the enemy forces.
Aron Nimzowitsch first recognized the power of a major piece on an open file, writing in his famous book My System that the main objective of a rook or queen on an open file is "the eventual occupation of the 7th or 8th rank".
White then used the open file to deploy his rooks to the seventh and eighth ranks and win the game, by exploiting the weakness of Black's a-pawn.
White's dominance on the d-file allowed him to maneuver his rooks to aggressive posts deep within Black's defense.