As mentioned above, the transcendental vibration oṁkāra is explained in the Bhagavad-gītā, Chapter Eight, verse thirteen:
oṁ ity ekākṣaraṁ brahma vyāharan mām anusmaran
yaḥ prayāti tyajan dehaṁ sa yāti paramāṁ gatim
"After being situated in this yoga practice and vibrating the sacred syllable oṁ, the supreme combination of letters, if one thinks of the Supreme Personality of Godhead and quits his body, he will certainly reach the spiritual planets." If one actually understands that oṁkāra is the sound representation of the Supreme Personality of Godhead, whether he chants oṁkāra or the Hare Kṛṣṇa mantra, the result is certainly the same.
The transcendental vibration of oṁkāra is further explained in the Bhagavad-gītā, Chapter Nine, verse seventeen:
pitāham asya jagato mātā dhātā pitāmahaḥ
vedyaṁ pavitram oṁkāra ṛk sāma yajur eva ca
"I am the father of this universe, the mother, the support and the grandsire. I am the object of knowledge, the purifier and the syllable oṁ. I am also the Ṛg, the Sāma and the Yajur Vedas."
(Sri Caitanya Caritamrta-----1:7:128-----purport).

Throughout all the Vedic literatures the glories of oṁkāra are specifically mentioned. Śrīla Jīva Gosvāmī, in his thesis Bhagavat-sandarbha, says that in the Vedic literature oṁkāra is considered to be the sound vibration of the holy name of the Supreme Personality of Godhead. Only this vibration of transcendental sound can deliver a conditioned soul from the clutches of māyā. Sometimes oṁkāra is also called the deliverer (tāra). Śrīmad-Bhāgavatam begins with the oṁkāra vibration: oṁ namo bhagavate vāsudevāya. Therefore oṁkāra has been described by the great commentator Śrīdhara Svāmī as tārāṅkura, the seed of deliverance from the material world. Since the Supreme Godhead is absolute, His holy name and His sound vibration oṁkāra are as good as He Himself. Caitanya Mahāprabhu says that the holy name, or oṁkāra, the transcendental representation of the Supreme Personality of Godhead, has all the potencies of the Personality of Godhead.
nāmnām akāri bahudhā nija-sarva-śaktis
tatrārpitā niyamitaḥ smaraṇe na kālaḥ
All potencies are invested in the holy vibration of the holy name of the Lord. There is no doubt that the holy name of the Lord, or oṁkāra, is the Supreme Personality of Godhead Himself. In other words, anyone who chants oṁkāra and the holy name of the Lord, Hare Kṛṣṇa, immediately meets the Supreme Lord directly in His sound form. In the Nārada Pañcarātra it is clearly said that the Supreme Personality of Godhead Nārāyaṇa personally appears before the chanter who engages in chanting the aṣṭākṣara, or eight-syllable mantra, oṁ namo nārāyaṇāya. A similar statement in the Māṇḍūkya Upaniṣad declares that whatever one sees in the spiritual world is all an expansion of the spiritual potency of oṁkāra.
(Sri Caitanya Caritamrta-----1:7:128-----purport).

On the basis of all the Upaniṣads, Śrīla Jīva Gosvāmī says that oṁkāra is the Supreme Absolute Truth and is accepted as such by all the ācāryas and authorities. Oṁkāra is beginningless, changeless, supreme and free from deterioration and external contamination. Oṁkāra is the origin, middle and end of everything, and any living entity who thus understands oṁkāra attains the perfection of spiritual identity in oṁkāra. Oṁkāra, being situated in everyone's heart, is īśvara, the Supreme Personality of Godhead, as confirmed in the Bhagavad-gītā (18.61): īśvaraḥ sarva-bhūtānāṁ hṛd-deśe ’rjuna tiṣṭhati. Oṁkāra is as good as Viṣṇu because oṁkāra is as all-pervasive as Viṣṇu. One who knows oṁkāra and Lord Viṣṇu to be identical no longer has to lament or hanker. One who chants oṁkāra no longer remains a śūdra but immediately comes to the position of a brāhmaṇa. Simply by chanting oṁkāra one can understand the whole creation to be one unit, or an expansion of the energy of the Supreme Lord: idaṁ hi viśvaṁ bhagavān ivetaro yato jagat-sthāna-nirodha-sambhavāḥ. "The Supreme Lord Personality of Godhead is Himself this cosmos, and still He is aloof from it. From Him only this cosmic manifestation has emanated, in Him it rests, and unto Him it enters after annihilation." (S.B.1:15:20) Although one who does not understand concludes otherwise, Śrīmad-Bhāgavatam states that the entire cosmic manifestation is but an expansion of the energy of the Supreme Lord. Realization of this is possible simply by chanting the holy name of the Lord, oṁkāra.
(Sri Caitanya Caritamrta-----1:7:128-----purport).

One should not, however, foolishly conclude that because the Supreme Personality of Godhead is omnipotent, we have manufactured a combination of letters—a, u and m—to represent Him. Factually the transcendental sound oṁkāra, although a combination of the three letters a, u and m, has transcendental potency, and one who chants oṁkāra will very soon realize oṁkāra and Lord Viṣṇu to be nondifferent. Kṛṣṇa declares, praṇavaḥ sarva-vedeṣu: "I am the syllable oṁ in the Vedic mantras." (B.G.7:8) One should therefore conclude that among the many incarnations of the Supreme Personality of Godhead, oṁkāra is the sound incarnation. All the Vedas accept this thesis. One should always remember that the holy name of the Lord and the Lord Himself are always identical (abhinnatvān nāma-nāminoḥ (CC.2:17:133). Since oṁkāra is the basic principle of all Vedic knowledge, it is uttered before one begins to chant any Vedic hymn. Without oṁkāra, no Vedic mantra is successful. The Gosvāmīs therefore declare that praṇava (oṁkāra) is the complete representation of the Supreme Personality of Godhead, and they have analyzed oṁkāra in terms of its alphabetical constituents as follows:
a-kāreṇocyate kṛṣṇaḥ sarva-lokaika-nāyakaḥ
u-kāreṇocyate rādhā ma-kāro jīva-vācakaḥ
Oṁkāra is a combination of the letters a, u and m. A-kāreṇocyate kṛṣṇaḥ: the letter a (a-kāra) refers to Kṛṣṇa, who is sarva-lokaika-nāyakaḥ, the master of all living entities and planets, material and spiritual. Nāyaka means "leader." He is the supreme leader (nityo nityānāṁ cetanaś cetanānām (Kaṭha Upaniṣad 2.2.13)). The letter u (u-kāra) indicates Śrīmatī Rādhārāṇī, the pleasure potency of Kṛṣṇa, and m (ma-kāra) indicates the living entities (jīvas). Thus oṁ is the complete combination of Kṛṣṇa, His potency and His eternal servitors. In other words, oṁkāra represents Kṛṣṇa, His name, fame, pastimes, entourage, expansions, devotees, potencies and everything else pertaining to Him. As Caitanya Mahāprabhu states in the present verse of Śrī Caitanya-caritāmṛta, sarva-viśva-dhāma: oṁkāra is the resting place of everything, just as Kṛṣṇa is the resting place of everything (brahmaṇo hi pratiṣṭhāham).
(Sri Caitanya Caritamrta-----1:7:128-----purport).

Every Vedic mantra is called brahma because each mantra is preceded by the brahmākṣara (aum or oṁkāra). For example, oṁ namo bhagavate vāsudevāya. Lord Kṛṣṇa says in Bhagavad-gītā (7.8), praṇavaḥ sarva-vedeṣu: "In all the Vedic mantras, I am represented by praṇava, or oṁkāra." Thus chanting of the Vedic mantras beginning with oṁkāra is directly chanting of Kṛṣṇa's name. There is no difference. Whether one chants oṁkāra or addresses the Lord as "Kṛṣṇa," the meaning is the same, but Śrī Caitanya Mahāprabhu has recommended that in this age one chant the Hare Kṛṣṇa mantra (harer nāma eva kevalam (CC.1:17:21). Although there is no difference between Hare Kṛṣṇa and the Vedic mantras beginning with oṁkāra, Śrī Caitanya Mahāprabhu, the leader of the spiritual movement for this age, has recommended that one chant Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare.
(Srimad Bhagavatam-----6:5:26-----purport).

The light of the sun and the moon is also originally emanating from the brahma-jyotir, which is the impersonal effulgence of the Lord. And praṇava, or the oṁkāra transcendental sound in the beginning of every Vedic hymn, addresses the Supreme Lord. Because the impersonalists are very much afraid of addressing the Supreme Lord Kṛṣṇa by His innumerable names, they prefer to vibrate the transcendental sound oṁkāra. But they do not realize that oṁkāra is the sound representation of Kṛṣṇa. The jurisdiction of Kṛṣṇa consciousness extends everywhere, and one who knows Kṛṣṇa consciousness is blessed. Those who do not know Kṛṣṇa are in illusion, and so knowledge of Kṛṣṇa is liberation, and ignorance of Him is bondage.
(Bhagavad-Gita-----7:8-----purport).

As far as the oṁkāra (praṇava) is concerned, it is considered to be the sound incarnation of the Supreme Personality of Godhead. As such, oṁkāra is eternal, unlimited, transcendental, supreme and indestructible. He (oṁkāra) is the beginning, middle and end, and He is beginningless as well. When one understands oṁkāra as such, he becomes immortal. One should thus know oṁkāra as a representation of the Supreme situated in everyone's heart. One who understands oṁkāra and Viṣṇu as being one and the same and all-pervading never laments in the material world, nor does he remain a śūdra.
Although He (oṁkāra) has no material form, He is unlimitedly expanded and has unlimited form. By understanding oṁkāra one can become free from the duality of the material world and attain absolute knowledge. Therefore oṁkāra is the most auspicious representation of the Supreme Lord. Such is the description given by the Māṇḍūkya Upaniṣad. One should not foolishly interpret an Upaniṣadic description and say that it is because the Supreme Personality of Godhead cannot appear Himself in this material world in His own form that He sends His sound representation (oṁkāra) instead. Due to such a false interpretation, oṁkāra has come to be considered something material, and consequently oṁkāra is misunderstood and eulogized as being simply an exhibition or symbol of the Lord. Actually oṁkāra is as good as any other incarnation of the Supreme Lord.
The Lord has innumerable incarnations, and oṁkāra is one of them, in the form of a transcendental syllable. As Kṛṣṇa states in the Bhagavad-gītā (9.17): "Among vibrations, I am the syllable om." This means that oṁkāra is nondifferent from Kṛṣṇa. Impersonalists, however, give more importance to oṁkāra than to the Personality of Godhead, Kṛṣṇa. But the fact is that any representational incarnation of the Supreme Lord is nondifferent from Him. Such an incarnation or representation is as good spiritually as the Supreme Lord. Oṁkāra is therefore the ultimate representation of all the Vedas. Indeed, the Vedic mantras or hymns have transcendental value because they are prefixed by the syllable om. The Vaiṣṇavas interpret oṁkāra, a combination of the letters a, u and m, as follows: By the letter a, Kṛṣṇa, the Supreme Personality of Godhead, is indicated; by the letter u, Kṛṣṇa's eternal consort, Śrīmatī Rādhārāṇī, is indicated; and by the letter m, the living entity, the eternal servitor of the Supreme Lord, is indicated. Śaṅkara has not given such importance to oṁkāra. But such importance is given in the Vedas, the Rāmāyaṇa, the Purāṇas and the Mahābhārata, from beginning to end. Thus the glories of the Supreme Lord, the Supreme Personality of Godhead, are declared.
(Teachings of Lord Caitanya).