Wiktionary
n. (context chess English) A file with only pawns of one color on it.
Wikipedia
In chess, a half-open file (or semi-open file) is a file with only pawns of one color. The half-open file can provide a line of attack for a player's rook or queen. A half-open file is exploited by the player with no pawns on it.
Many openings, such as the Sicilian Defense, aim to complicate the position. In the main line Sicilian, 1.e4 c5 2.Nf3 d6 (or 2...e6, or 2...Nc6) 3.d4 cxd4 4.Nxd4, White obtains a half-open d-file, but Black can pressure White along the half-open c-file.
The demolition of the pawn structure is a common theme in positions with half-open files, since doubled pawns or isolated pawns may create half-open files.
Usage examples of "half-open file".
Qwilleran's eyes, known for their doleful expression and drooping lids, roamed over the clutter on the editor's desk, the crumpled paper that had missed the wastebasket, the half-open file drawers, the stacks of out-of-town newspapers.