In Hinduism and Buddhism Aum is the most basic mantra, which in Hinduism is known as the "pranava mantra," the source of all mantras because it is the "all-sound" or the sound of which all other sounds are but modifications. It is the sound of the entire cosmos and the entire circle of time.
The mantra "Aum" was first spelled "Om" in the West and it is this spelling that is still most commonly encountered. However, the alternate spelling of "Aum" is being used with increasing frequency because it is more phonetically accurate.
If intoned correctly, the mantra does not rhyme with "home" or "Tom" as one may be inclined to pronounce "Om". Rather, "Aum" is pronounced in such a way that it produces the entire range of what is called an "envelope" in sound engineering. An envelope is precisely what is created by using a "wah-wah" pedal with an electric guitar, or the effect one gets from cupping one's hand over one's ears and then lifting the hands from the ears as one would lift a lid. An envelope ranges from the widest and most open sound to the most narrow and finally to a closed and muffled bass sound, like that of humming with the lips completely closed.
"Aum" starts the wide-open sound of "aaahh" which should be made with the mouth wide open and the tongue flat against the bottom of the mouth to the sound "ooooo" (rhyming with "blue") which is not wide but deep and more condensed with the lips pushed out and in the form of a circle so that the mouth cavity forms a tube out of which comes the "ooooo" sound and finally the lips are pulled back and closed to form the final "mmmmm" sound. These sounds should blend seamlessly together, with a long "O" sound (rhyming with "low") blended between the "aaahh" and "ooooo" before moving on to the "mmmmm" sound.
In the cosmology of Hinduism, this represents entire cycle of the universe first bursting forth from nothing, expanding out in all directions and finally contracting back again into nothing. This is called the Trimurti or three stages of the cosmos, sometimes expressed as creation, preservation and destruction and personified (or deified) by the three gods Brahma ("the Creator"), Vishnu ("the preserver") and Shiva ("the Destroyer"). Together, the entirety of this process encompasses the life-time of Brahman, or existence itself which in Hinduism is calculated to be approximately 311,040,000,000,000 terrestrial years.
This is an approximate parallel of the cosmology of the Big Bang theory with the A in "Aum" representing the "bang", the explosion or expansion, the U representing the equilibrium in which atoms, molecules, stars, planets and life can form and be sustained and the M representing the "Big Crunch" in which the whole universe will be drawn back together as the sum total of all gravity then takes over until the entire universe condenses back into nothing.
The three letters in "Aum" can be taken to represent any ultimate tripartite process such as, in alchemy, dissolution, purification and unification (solve et coagula) or process in the formula of IAO (http://www.thelemapedia.org/index.php/IAO), the larval, pupal and adult stages of insect life, the birth, life and death of all living beings, or the beginning, middle and end of all processes whatsoever from subatomic particles rising from the void, existing for an infinitesimally short period of time before disappearing again to the entire duration of time itself.