The number 108 is very auspicious for Hindus. It is the number of beads of a rosary and of many other things in Indian cosmology. But why is this number considered to be holy?
The answer to this mystery may lie in the fact that the ancient Indians took this to be the distance between the earth and the sun in sun-diameter units and the distance between the earth and the moon in moon-diameter units.
Two facts that any book on astronomy will verify :
Distance between earth and sun = 108 times sun-diameter
Distance between earth and moon = 108 times moon-diameter
The reason why we do our mantra jaap 108 times is because its a symbol of our journey towards our higher/spiritual self (sun) from our material self (earth).