Several definitions exist for the word "Maze"; see Labyrinth for several examples through history.
Mainly, the idea is that there are a set of rooms linked by doors (so a passageway is just another room in this definition). You enter at one spot, and exit at another, or the idea may be to reach a certain spot in the maze.
Mazes have been built in buildings with walls and rooms or "built" by growing hedges or crops such as corn.
Alternatively, they can be drawn on paper to be followed by pencil, or built of paving stones of contrasting colors or designs to be followed on foot.
One of the short stories of Jorge Luis Borges dealt with the concept of a book which was a literary maze.
Various Maze generation algorthims exist for building mazes, either by hand or by computer.