According to Swami Vivekananda, the great masters or “siddha-gurus”, pass on spiritual wisdom to disciples through mantras. The sacred mantra "OM", or A-U-M, represents the entire universe. Brahma, the “Creator aspect” of the holy Hindu Trinity, manifested himself as name and form, the form being this universe. OM is the name or word representing the thought out of which the universe was created.

In the Gospel of John it says, “In the beginning was the Word, and the Word was with God, and the Word was God”. In the Mandukya Upanishad it says, “Om. This eternal Word is All: what was, what is and what shall be, and what beyond is in eternity. All is Om.”

The three letters A-U-M, pronounced in combination as OM, symbolize all sound vibrations, which therefore resonates in all creatures of the Universe. The "A" sound comes from the back of the throat at the root of the tongue. The "M" sound is when the sound ends at the lips, in a humming sound. In between these two is the "U" sound, from the width and wholeness of the mouth, the "rolling forward" of the sound from the root to the lips. OM, therefore, represents the whole range of sound production, and no other word can do this. OM is the true symbol of God and the Universe.

In the Prasna Upanishad, it is said that when "one meditates on OM and remains in steadiness, purity and truth, he/she attains greatness." "The syllable "OM", when it is not fully understood, does not lead beyond mortality. When it is fully understood, and meditation is therefore rightly directed, one is freed from fear, whether he/she be awake, dreaming, or sleeping in dreamless sleep and attains to Brahman." "By virtue of little understanding of OM, one returns to earth after death. By virtue of a greater understanding one attains to the celestial sphere. By virtue of complete understanding of OM, one learns what is known only to the seers. The sage, with the help of OM, reaches Brahman, the fearless, the undecaying, the immortal!"

Here are some representations of A-U-M.
A= the state of waking consciousness.
U= the state of dreaming consciousness.
M= the state of sleeping consciousness.
AUM or OM is the state of supreme consciousness.

A= the past, U= the present, M= the future

A= coming from the lower lungs, U= coming from the middle lungs, M= coming from the upper lungs

A= omnipotent or all powerful, U= omnipresent or all pervading, everywhere, M= omniscience or all knowing

Swami Sivananda says, "The Lord willed and there was a vibration. The world was projected. The sound OM was emanated." He suggests this exercise: Have a picture of OM in front of you. Concentrate gently on this picture with open eyes till the tears flow profusely.

Associate the ideas of eternity, infinity, and immortality with OM. All sounds, such as bees humming, birds singing, the musical notes, all emanate from OM. OM is the essence of the Vedas (the oldest sacred texts). Imagine that OM is the bow, the mind is the arrow, and Brahman or God is the target. Aim at the target with great care, and then, like the arrow becomes one with the target, you will become one with Brahman.

The short accent of OM burns all sins. The long accent of OM gives Moksha, or liberation. The elongated accent bestows all siddhis or psychic powers. When one chants and meditates upon this monosyllable OM, one chants and meditates upon all the Scriptures of the world.

References:
The Yogas and Other Works - by Swami Vivekananda;
Practical Lessons in Yoga - by Swami Sivananda;
The Upanishads - Translated by Juan Mascaro
The Holy Bible