Meaning of AUM
A sacred sound symblizing purity of pranava mahamantra. A cosmic vibration. According to Indian spiritual sciences, God first created sound, and from these sound frequencies came the phenomenal world. Our total existence is constituted of these primal sounds, which give rise to mantras when organized by a desire to communicate, manifest, invoke or materialize.
Matter itself is said to have proceeded from sound and AUM is said to be the most sacred of all sounds. It is the syllable which preceded the universe and from which the gods were created. It is the “root” syllable (mula mantra), the cosmic vibration that holds together the atoms of the world and heavens. Indeed the Upanishads say that AUM is god in the form of sound. Thus AUM is the first part of the most important mantras
Another ancient text equates AUM with an arrow, laid upon the bow of the human body (the breath), which after penetrating the darkness of ignorance finds its mark, namely the lighted domain of True Knowledge. Just as a spider climbs up its thread and gains freedom, so the yogis climb towards liberation by the syllable AUM.
Meaning
Om denotes the supreme Brahma:
omiti brahma omitīdaṃsarvam [Tait. Up. – 1.8.1]
Om is Brahman. Om is everything here
.girām asmy ekam akṣaram [BG – 10.25]
Of sound vibrations I am the single syllable (OM)
But as we know God is threefold is nature, same is the case for the single syllable Om. It consists of three differnt letters A, U, M which are the seed of all other letters, sounds and words.
sa vā eṣa omityetadātmābhavat sa tredhātmānaṃ vyākuruta omiti tisro mātrā etābhiḥ [Mait. Up. 6.3]
Meaning
He(God) came to have Om as his soul. He divided into three parts. So Om is the three units (a,u,m).
Significance
Now the letters of A,U,M can be signified differently as creation, preservation, annihilation, or satva(goodness),rajas(passion), tamas(ignorance). The Mandukya Upanishad which deals only the pranava (Om) defines the three units as below:
jāgaritasthāno vaiśvānaro’kāraḥ prathamā mātrā [Mandu. Up. – 9]
Waking state is the first unit (A)
svapnasthānastaijasa ukāro dvitīyā mātrā [Mandu. Up. – 10]
Dream state is the second unit (U)
suṣuptasthānaḥ prājño makārastṛtīyā mātrā [Mandu. Up. – 11]
Sleeping state is the third unit (M)
These three states are related to a person. But these are also synonymous to creation, preservation, annihilation and other meanings when analyzed from the universal point of view.