In some Native American cultures, a maze symbolizes mother earth, or more specifically a mother (nature) and child (us).  In some ancient cultures, the maze represented the souls journey into the afterlife.  In others, it represented man's journey of self discovery.  Some ancient cultures thouth mazes could trap evil spirits.  Some Christian churches adopted the mythology and put labyrinthine patterns on their floors.  Pilgrims follow the path and pray in a type of meditation ritual.  It this case, the maze, or labyrinth, represents the path to salvation.  The main idea seems to be that the maze, like life, offers us choices.  Make the right choices and escape the maze.  Make the wrong choices and stay trapped.
The best known myth about a labyrinth or maze is the story of the Minotaur.  The minotaur, trapped in the underground labyrinth, was killed by Theseus, who then escaped the maze by following a thread.  A symbol of the "thread of Life" perhaps?

The simpler spiral design is often considered a simplified version of a labyrinth and has the same meaning.   According to Joseph Campbell, the well known writer on mythology, The spiral is the most widely recognized and repeated archetype used to symbolize our inner and outer journey to God and the Self.   The spiral image defined for Jung the Gnostic Christian belief of a pleroma which is a void where there is nothing and everything and what exists within it is an eternal process.  It also is a solar symbol representing the sun spinning and sending out waves of energy - the solar wind.