The Japa-malas have 108 beads. What is the significance of 108 ?
The japa-mala teaches you the Unity, though it has 108 beads! If it is a sphatika maala (garland of crystal beads), you can see the string running in and through each bead, the inner reality on which all this is strung! If the beads are not transparent, you still know that the string passes through, holds together and is the basis for the maala to exist! Why 108 beads? 108 is the product when 12 is multiplied 9 times, 12 is the number of Adityas (luminaries), that reveal the objective world, and so, symbols of the Saakara aspect (the world of name and form, of manifoldness, the seeming variety, the fleeting pictures). 9 is the screen on which the pictures appear, the basis, the rope which deludes you as the snake in the dusk, Brahman, the Nameless, Formless, Eternal Absolute. 9 is the Brahman Number, for it is always 9, however many times you multiply it! It is immutable, for 9 multiplied by any number finally adds up to 9 only. So, when you turn the beads, impress upon yourself the fact that there is both truth and travesty in the world, that the travesty attracts, distracts and delights in deceiving you, diverts you into devious paths, the truth makes you free.
(SSS Vol 9, pg 28-29)