Fog is the light grey substance that is the lighting property which appears throughout Lumberland, and its purpose is to shorten players view ahead of them so they cannot see everything ahead.
The Fog increases during the in-game night (approximately 11 PM) and decreases at dawn (approximately 9 AM). Fog in places such as the Lost Cave, Maze, and End Times are special because the fog is much closer and darker than above the surface, but still appears to recede or fall in respectively to the time of day.
The Fog changed throughout the stages ALPHA & BETA, and in ALPHA the Fog was very little and believed to be only seen 6,000 studs away from a player. In BETA the fog increased throughout Lumberland, possibly only 1,000 studs from a players sight, and was a slightly lighter shade of purple than it is now. Later in the BETA stage, the Fog decreased to 300 studs away from a player and has been set like that ever since. It's now a firmed property of the game and likely will not change in the future.