answer by someone on Quora:
A lot of people, who draw or doodle mazes, do them either absent-minded or in a focused manner. For those who draw them without any particular thought, it’s likely an expression of the subconscious mind, where creativity usually reigns. It may be an attempt to gain a medium that breaks free of the rules of language or interpretation, through indirect symbolism. A maze can possibly represent a person’s feelings of confinement or emotional barriers. It may reflect a personal obstacle or challenge the doodler is experiencing, or it may be that the person is living too fast-paced & craves an opportunity to slow down. And regarding those who attempt to do them purposely, it’s typically an activity for those of an introverted or obsessive nature, as well of those who are simply fond of patterns that evolve. A maze also has a nice ambiguity in that it can be both structural, yet abstract. It expresses both the fear of getting lost, as well as the pleasure and challenge of exploration. These opposing meanings, not uncommon in symbols, explain partially our fascination with them. Mazes and labyrinths have been a part of human culture since 2500 BCE, and can be found all over historical sites around the world. Humans have always been fascinated by them, as they provide a person the willingness to get lost upon entering. Penelope Doob, a Stanford Professor and author, points out that mazes and labyrinths reward us for our persistence, memory, and intelligence. One can force you through a set journey, while another can deliberately seek to confuse and frustrate.