This has reference to Khushwant Singh's article in Deccan Herald on the mantras. Some important aspects of using mantras include:

" Repetition: A mantra can be repeated hundreds, thousands, or millions of times, depending on the individual's spiritual practice. Typically, aspirants repeat mantras in multiples of three with 108 being the most common multiple used (for numerological reasons). Repetition of a mantra is known as japa or mantra japa.

" Counting: It is important to focus on the meaning of the mantra rather than just count the number of times it is repeated. Hence, a bead necklace known as mala consisting of 108 beads is used as an external aid. The number 108 has significance on account of several reasons. For example, 108 is an integer divisible by the sum of its digits. The number of Upanishads is 108. The number of delusions that one has to conquer to attain enlightenment is said to add up to 108.

Another possible explanation is:
 
Q: Why do we say the Surya mantra 108 times, not 106 (?) and not 110 ?

 The answer is : Ancient Indian astronomers had calculated and deduced that 108 times the diameter of the earth is the diameter of the sun. The nine planets go round the twelve Zodiacal signs 108 times. The 27 stars      are divided each into four equal parts. Thus there are 108 parts of the twenty seven stars. A lotus flower has 108 petals. The importance of 108 almost certainly originated from the number of Upanishads:
 
Q: What are the scriptures of the Hindus? 
A Sruthi - that which is heard - are the Vedas ( 4 ) and the Upanishads ( 108 ).

Kapil Bhargava