A hunger puzzle is a form of timed puzzle that requires the player to find food at regular intervals, typically in order to prevent the PC from collapsing of exhaustion. Variations may include thirst, sleep, electrical charge (if the PC is a robot), etc.
When implemented well, a hunger puzzle can provide a short-term goal that advances the plot or otherwise rewards the player. When implemented simply in order to emulate the health statistics of RPG systems, or in order to extend gameplay by making a sequence more difficult than it would be otherwise, it rapidly becomes tedious. (of course, much the same caveat applies to many canonical and "done-to-death" puzzles, including the maze, light source, and inventory management puzzle.)