The importance of the number 108 in Sanatan Dharma from Vedic era is remarkable. The Indian scholars in vedic time were excellent mathematics scholars. This number is sacred since the vedic time and mentioned from the oldest texts we have.
1 stands for God or the higher truth, 0 stands for emptiness and completeness in spiritual practice and the 8 for the infinity and eternity.
The Sanskrit alphabet called Devanagari has 54 letters and each of them has feminine and masculine form. Hence that makes: 54 x 2 = 108
The rosary of the vedic time has 108 beads, Lord Krishna has 108 gopis or maid servant, we have 108 Upanishades. In the heart chakra (Anahata) we have intersections of energy lines, which are 108 to form the heart chakra. The important of the number 108 is also seen in the 108 names for Gods like Lord Shiva and many others.
There are 108 forms of dance in Indian tradition. In the Sree Yantra central point (Bindu), there are 3 lines intersecting and we have 54 intersections, each masculine and feminine. These 108 points defines the Sri Yantra and the human body.
The Vedic system says the universe is created by 5 elements; Space, Air, Fire, Water and Earth and they are the reason for 3 attributes; Birth, Protection and Destruction, They are called Guna in Sanskrit and known as Raja, Sata and Tama guna. This cycle has, according to mathematical and geographical evidence 360 degrees. This teaching is very much symbolic. If we take the space as the cycle and divide it by the 4 other elements and multiply them with the 3 attributes we get the idea of time. 3 x 4 = 12 and we have the number of months in a year and the half of a day by 12 hours. We have 27 Naksatra or fixed stars and added them to the 3 gunas, it forms our months of 30 days. The ancient sages counted only the day time and for the night they multiplied by 2. If we multiply our 360 degree by 30 we get 10800. The 0 was taken as complete, we need only take the first 3 numbers 108. The ancient Sages took the "108" as the representation of the complete universe.
By the offer and singing any mantra 108 times the respect towards the supreme is considered complete.