We chant OM to connect with our true Self. Since our true Self is the same as the Supreme Self, when we connect with our true Self we connect with the Supreme Self.
In Sanskrit, the sound "O" is a diphthong spelled "AU". AUM is comprised of three sounds: "A", "U" and "M". There is also a fourth sound which is a universal vibration and is the essence of all other sounds.
AUM represents many trilogies of meanings:
Symbolically the three letters embody the divine energy (Shakti) and it's 3 main characteristics:
(1) beginning of the universe
(2) the life period of universe
(3) destruction of the Universe
AUM is the word which represents the three first forms of God:
1) Brahmaa (Creator of universe)
2) Vishnu (Operator of universe)
3) Mahesh (Destructor of universe).
As per Mandukya Upanishad:
1) The "A" stands for the state of wakefulness, where we experience externally through our mind and sense organs.
2) The "u" stands for the dream state, in which inward experiences are available.
3) In the state of deep sleep, represented by the sound "m", there is no desire and consciousness is gathered in upon itself.
AUM is the one eternal syllable of which all that exists is but the development. The past, the present, and the future are all included in this one sound, and all that exists beyond the three forms of time is also implied in it.
Earth, Atmosphere, and Heaven.