I came across an informative and interesting piece on Yoga Journal called “The Number 108”, written by Shiva Rea – she teaches prana vinyasa flow and yoga trance dance all over the world and is part of the Yoga Journal team. Someone asked Yoga Journal what the significance of the number 108 is in order to understand why people sometimes undergo the challenge of practicing 108 sun salutations. Shiva Rea’s answer was:
The number’s significance is open to interpretation. But 108 has long been considered a sacred number in Hinduism and yoga. Traditionally, malas, or garlands of prayer beads, come as a string of 108 beads (plus one for the “guru bead,” around which the other 108 beads turn like the planets around the sun). A mala is used for counting as you repeat a mantra—much like the Catholic rosary.
Renowned mathematicians of Vedic culture viewed 108 as a number of the wholeness of existence. This number also connects the Sun, Moon, and Earth: The average distance of the Sun and the Moon to Earth is 108 times their respective diameters. Such phenomena have given rise to many examples of ritual significance.
According to yogic tradition, there are 108 pithas, or sacred sites, throughout India. And there are also 108 Upanishads and 108 marma points, or sacred places of the body.
Hope this helps!