In most basic terms, a puzzle involving a set of rooms that is usually more difficult to navigate because of some shared complexity in their design. Early mazes tended to feature similar or identical room descriptions and non-reciprocal passages: going west from room 1 led you to room 2, but the way back to room 2 from room 1 was south, and so on. Subsequent variations include rooms that have to be tranversed in a particular order, rooms in which the normal compass directions are non-functional, and so on.
There are three basic types of mazes, dating from the earliest of text adventures: those with non-identical room descriptions, in which it has to be recognized by the player that the description is unique to the room, and which will be repeated at the "verbose" description setting; those with identical room descriptions, which are discernable by dropping an object from inventory in a room, and hoping that a non-player character does not steal it as you move about trying to map the connections on a piece of paper; and mazes whose room connections change while you are trying to solve the maze, perhaps as a result of something you did before entering the maze, or something you did while in the maze, or by a built-in random reconnection subroutine. The first two types of mazes appear in Advent (Colossal Cave).
Generally, these days such puzzles are looked upon as dull and repetitive in nature.
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