The number 108 is sacred in Hindu philosophy as a number of completeness frequently associated with astrology. The average distance between the Earth and the moon is approximately 108 times the diameter of the moon (More accurately, 110), and the same relationship exists between the Earth and the Sun (107.8 to be exact). This is why the Sun and the moon appear the same size. Also, there are 9 planets and 12 Zodiac constellations, so there are 108 possible ways to place a planet in a constellation.
In Indian culture there are many instances of the number 108. There are 108 sheperdesses who followed Lord Krishna, 108 beads on the rosary, and there also are said to be 108 Upanishads, even though the actual number exceeds 200. Devotees often chant mantras 108 times.
According to the Tantra, there are 108 pilgrimage centers that are dedicated to the feminine/lunar principle. This is the story of their creation:
Source - http://www.yrec.org/108.html
The Golden Age had passed, and a less perfect age was in motion. God Shiva, heavenly prototype of ascetics and yogis, was constantly absorbed in deepest meditation. His austerities caused such heat that the universe was threatened with extinction. Brahma, the Creator, was understandably worried. He begged the Great Goddess to distract Shiva from his yogic efforts and engage him in love play, so that creation could continue to exist. The Mother of the Universe agreed to take human form in order to entrance Shiva, her beloved. She entered the womb of Vîrinî, Daksha's wife, to be born as Satî ("She who is").
Satî was the first-born of the sixty daughters of Daksha. With the power of the Goddess within her, she succeeded in arousing Shiva's interest not only by her exquisite beauty but also by her asceticism. He asked her to be his wife and even assumed human form by her sake. When her father, Daksha, insulted Shiva at a feast, she entered into deep meditation and immolated herself.
Shiva, grief-stricken, recovered her partially consumed body from the flames of the sacrificial fire and bore it away into heaven. Fragments of her body fell to earth in 108 different places over the Indian subcontinent, filling each site with her holy presence. In time, these locations became places of Goddess worship.
The three best known sites are the pîthas near Calcutta, Kâmâkhyâ in Assam, and Jâlandhara, which are said to be the locations of Satî's big toe, womb, and breast respectively. Historically, the earliest Tantric scriptures mention only four pîthas. Over time, these seem to have grown to first 51 (said to actually contain the relics of Satî) and later 108. Satî's self-immolation is the mythological core of the Hindu custom of suttee (from Satî), where the widow enters the funeral pyre of her husband. This tradition was banned during the British rule in India.