108, or 3x3x12, is a very sacred number throughout the world. For example in Hinduism, Buddhism, Jainism and Catholicism rosaries or their Eastern equivalents almost invariably consist of 108 beads. In Hinduism the chakra system consists of 114 centers, just as the Qur'an contains 114 surahs (chapters); but, because many of these lie outside the body or are otherwise unworkable, there are 108 chakras used in practice.
There is an Oriental alchemical myth in which a green dragon (presumably the green lion of regeneration) guards a great treasure (the Philosopher's Stone): this dragon has 108 scales, 54 to the Yin and Yang natures. (See: Alchemy)
108 in Nature
108 is 1/10th the radius of the Moon and 1/400th the radius of the Sun in miles. The distance between the Earth and Sun is roughly 108 Earths at any given time, so too with the Moon.
108 in Scripture
The Bible contains many obscure references to this number, most of which are only accessible via Qabalistic or other cryptic permutations. For example 108/2 and 108x2 both appear in the 216-letter permutation of Leviticus that reveals the 72 Names of God. (Interestingly this passage might also be interpreted as referring to the Moon.)
It is also seen in the most well-known of Equidistant Letter Sequences, that discovered by Rabbi Weissmandel in the Pentateuch, or Five Books of the Law of Moses. ELSs are quite controversial and many choose to reject the notion that they were intentionally created and/or embedded in the Bible. An ELS is obtained as follows: one selects a letter, skips a fixed number of letters (excluding spaces), and then selects a second letter, to skip the same number again until something ideally coherent emerges. The Rabbi's read Torah twice with an ELS of 50, (one in Genesis, the other in Exodus), then in the third book (Leviticus) it read Yahweh with one of 8, then Torah twice in the next two books (Numbers and Deuteronomy) with the same ELS, but backward this time.
Apart from the inherent unlikelihood of this particular sequence, one might also observe that TORH + TORH + YHWH = 108 x 4 = 432 (because each letter has an ELS of 50 or 8). This is remarkably significant and is not easily explainable.