Aum just comes from the combination of two letters of the old Indian alphabets. “Au” comes from what we call “oora” in punjabi — it even looks like Aum. That’s the you get when your mouth is fully open without any obstruction. “M” is the last alphabet in the old Indian system. It is the sound we make when our mouth is fully obstructed.
I find interesting that in other language and religious systems the same emphasis is paid to the beginning and ending letters of the alphabet. It is also interesting to note how the beginning and end is related to “truth” in many different cultures. See the following notes from Wikipedia:
Alpha and Omega
Alpha and Omega, alpha (α or Α) and omega (ω or Ω), are the first and the last letters of the Greek alphabet and are an appellation of Christ or of God in the Book of Revelation. These couple of letters are used as Christian symbols, and are often combined with the Cross, Chi-rho, or other Christian symbols.
The term Alpha and Omega comes from the phrase “I am the alpha and the omega” (Koiné Greek: τὸ Α καὶ τὸ Ω), an appellation of Jesus in the Book of Revelation (verses 1:8, 21:6, and 22:13). The first part of this phrase (“I am the Alpha and Omega”) is first found in Chapter 1 verse 8, and is found in every manuscript of Revelation that has 1v8. Several later manuscripts repeat “I am the Alpha and Omega” in 1v11 too, but it does not receive support here from most of the oldest manuscripts, including the Alexandrine, Sinaitic, and Codex Ephraemi Rescriptus. It is, therefore, omitted in some modern translations. Scholar Robert Young stated, with regard to “I am the Alpha and Omega” in 1v11, that the “oldest [manuscripts] omit” it.
Meaning in Christianity
Its meaning is found in the fact that alpha (Α) and omega (Ω) are respectively the first and last letters of the Classical (Ionic) Greek alphabet. This would be similar to referring to someone in English as the “A and Z”. Thus, twice when the title appears it is further clarified with the additional title “the beginning and the end” (Revelation 21:6, 22:13).
Though many commentators and dictionaries apply this title both to God and to Christ, some secular sources argue otherwise. Barnes’ Notes on the New Testament (1974) claims: “It cannot be absolutely certain that the writer meant to refer to the Lord Jesus specifically here … There is no real incongruity in supposing, also, that the writer here meant to refer to God as such.”  Most Christian denominations also teach that the title applies to both Jesus and God.
The letters Alpha and Omega in juxtaposition are often used as a Christian visual symbol (see examples). The letters were shown hanging from the arms of the cross in Early Christian art, and some crux gemmata, jeweled crosses in precious metal, have formed letters hanging in this way, called pendilia. In fact, despite always being in Greek, the letters became more common in Western than Eastern Orthodox Christian art. They are often shown to the left and right of Christ’s head, sometimes within his halo, where they take the place of the christogram used in Orthodox art.
This symbol was suggested by the Apocalypse, where many believe that Christ, as well as the Father, is “the First and the Last” (ii, 8); “the Alpha and Omega, the first and the last, the beginning and the end” (cf., xxii, 13; i, 8). Clement of Alexandria (2nd century, philosopher and commentator on pagan and Christian information) speaks of the Word as “the Alpha and the Omega of Whom alone the end becomes beginning, and ends again at the original beginning without any break” (Stromata, IV, 25). Tertullian (lawyer, theologian) also alludes to Christ as the Alpha and Omega (De Monogamiâ, v), and from Prudentius (Cathemer., ix, 10) we learn that in the fourth century the interpretation of the apocalyptic letters was still the same: “Alpha et Omega cognominatus, ipse fons et clausula, Omnium quae sunt, fuerunt, quaeque post futura sunt.” It was, however, in the monuments of early Christianity that the symbolic Alpha and Omega had their greatest vogue.
This phrase is interpreted by many Christians to mean that Jesus has existed for all eternity. The phrase “alpha and omega” may signify that God is eternal. The symbols were used in early Christianity and appear in the Roman catacombs.
In Rabbinic literature, the word emet (אמת meaning “truth”), one of the names of God in Judaism, has been interpreted as consisting of the first, middle and final letters of the Hebrew alphabet.
The Qur’an gives al’Awwal (الأول), meaning “The First” and al’Akhir (الأخر), meaning “The Last” as two of the names of God: 57:3.