The e-file is an open file since there are no pawns on it. The rook can move to any square on the file (marked with crosses), uninhibited by pawns.
An open file in chess is a file with no pawns of either color on it. In the diagram, the e-file is an open file. An open file can provide a line of attack for a rook or queen. Having rooks or queens on open files or half-open files is considered advantageous, as it allows a player to attack more easily, since a rook or queen can move down the file to penetrate the opponent's position.
A common strategic objective for a rook or queen on an open file is to reach its seventh or eighth rank (the opponent's second or first rank). Controlling the seventh rank is generally worth at least a pawn, as it threatens all the opponent's yet-unmoved pawns to some degree. 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".
Many games are decided based on this strategy. In the game Anand–Ivanchuk, Amber 2001, Anand sacrificed a pawn to open the d-file. 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.
Anand vs. Ivanchuk, 2001: Example of creating and exploiting an open file
^According to Nimzowitsch, "A file is said to be open for the Rook when no pawn of his [own color] is in it." Elsewhere, "From the definition of an open file, it follows that a file will be opened by the disappearance of one of our own pawns." This defines what others call a half-open file.