The number 108 has different meanings in different religions. It represents wholeness. There are 54 letters in the Sanskrit alphabet, and each letter has a masculine and feminine quality so wholeness is 54+54=108.
In Buddhism, there are said to be six senses, the five physical senses and one mental sense (the mind). Each sense can have 3 states: neutral, pleasant and unpleasant. There are therefore 18 sense-states. These states can exist in the past present or future, making 54 temporal (time related) conditions. There are two ways of responding to these conditions, making 108 possible responses to the conditions.
There are said to be 108 different audible prayers or mantras, which are counted using the beads.
Other meanings for 108 relate to the number of planets in our solar system (taken to be 9) and the number of signs in the zodiac (12), the combination being 9 times 12=108. 12 is also the number of months (moons) in a year, and, in turn, this relates to the menstrual cycle, which is obviously rrelated to human life. So 108 has astrological and astronomical significance. It also happens that there are about 108 sun-diameters between the earth and our sun and about 108 moon-diameters between the earth and our moon. (The distances between the earth and the moon, and between the earth and the sun do vary because the orbits of the moon and earth are not perfectly circular, while the diameters remain constant.)
Perhaps another interesting property of 108 is that it is made up of the first two prime numbers (2 and 3): 108=22×33 (note that the exponents are also the first two prime numbers). Prime suggests primeval or primordial, which relates to the beginning of time and history. This adds the dimension of time as well as space to the meaning of 108, emphasising the sense of wholeness.