Mr. Iyengar writes in Light on Yoga about the Sanskrit word AUM and the Latin word Omne both being derived from the same root where both words convey the concepts of omniscience (all knowing), omnipresence (all-pervading) and omnipotence(all-powerful).
He writes that another word for Aum is pranava and is derived from the root nu meaning praise and the pra prefix means superiority, so the meaning is the best praise or prayer.
The symbol AUM is composed of three syllables and carries many meanings.
The A symbolizes the conscious or waking state, the U the dream state and the letter M the dreamless, sleep state.
The entire symbol with the crescent and dot stands for the fourth state which transforms all the states and transcends them to the state of Samadhi.
The letters also represent speech, mind and breath of life and the entire symbol is the living spirit.
The letters are also said to represent length, breadth and width, while the whole symbol represents Divinity going beyond the limitations of shape and form.
Mr. Iyengar gives many more meanings of the word and symbol AUM.
A few others are:
A,U, M symbolise the absence of desire, fear and anger and the whole symbol represents the perfect being.
A, U, M represents the three gunas of sattva, rajas and tamas and the symbol represents the gunatita or the one who has transcended the pull of the gunas.
There are a few more references regarding the meaning of AUM and from this Mr. Iyengar writes that the yogi realizes the importance of AUM and focusing on it with one-pointed devotion to experience the feeling and meaning of the mantra.