Half-open files arise naturally from pawn exchanges and from openings like the Sicilian, where Black trades the c-pawn and gains a half-open c-file to operate on. The side with the open side of the file aims a rook at the enemy pawn that sits on it, often combining the pressure with a minority attack or a piece maneuver to win or fix that pawn.
Working the half-open file is a long-term plan: even if you cannot win the target pawn immediately, the constant pressure ties the opponent's pieces to its defense, granting you freedom to operate elsewhere. Many opening choices are made specifically to obtain a useful half-open file.