When using a maze, a child must learn the fine motor skill of a pincer grasp (using forefinger and thumb) to move the beads from one end to the other.  This grasp is the pre-cursor to writing.
Moving the beads through the loops and twirls introduces the child to object permanence and they look for the bead and continue to play - this gives rise to hand-eye coordination as well as increasing their attention span.  
The variety of shapes is the start of geometry (maths skills).  As well, these shapes as well as colour labelling gives rise to an increased vocabulary.