It is the smallest mantra (मंत्र; mantraa). It is also called pranav-mantra. Probably pranav (प्रणव; praNNav) means primordial (मूल; mool).
A mantra is a word or a phrase used for meditation and chanting.
A shloka (श्लोक; shlok) is a verse. Generally people use the words - mantra and shloka as synonyms!
Sacred ancient Indian texts like Vedas (वेद; ved), are collections of shlokas. Some of these shlokas are used as mantras.
It is a common practice to begin other mantras with Om. E.g. Om Namah Shivaya (ॐ नमः शिवाय; Om namah shivaaya), Om Shanti Shanti (ओम शांति शांति; Om shaanti shaanti).
Jainism, Buddhism and Sikhism originated from India after Hinduism. These religions adopted lots of Hindu philosophies and practices. These religions have their own form and understanding of Om. Religious minded Hindus believe that Om is the ultimate, hyper or super-natural sound!
Using DevaNagari alphabet, this word can be written as ओम् or ओम. It is general practice in DevaNagari to drop the last halant (i.e. ्). So ओम is generally preferred over ओम्.
Generally the spelling ओम is used in literature (as noun); while the sign/symbol ॐ is used for religious purposes.
The Meaning of Om or AUM
Some of us are not yet very sure of the precise meaning of the word Om! It is certainly related to the God/Heaven!
Twelve verses of ved collectively called माण्डूक्य उपनिषद (maandookya Upanishad) tries to explain this sacred word Om or AUm (अ-उ-म्).
As per the Sanskrit/Hindi grammar (vyaakaraNN; व्याकरण) the vowel O (ओ) is sometimes substituted for two consecutive vowels A (अ) and U (उ); Generaly public too prefer Om instead of AUM (AUm)!
Gayatri Mantra (गायत्री मंत्र; gaayatree maNtra) like many other vedik shlokasstarts with Om. Thats why I assumed that Om (ओम) means My Lord or Oh, our God (हे परमेश्वर); I may be wrong.
Some people say there is a relation between the words Om and Amen; others doubt it!
The Om symbol - ओंकार
An Om symbol is a sign (glyph, shape) to write (scribe, represent) the Om sound.
Om symbol is called Omkar (ओम्-कार; Omkaar) or Onkar (ओंकार; ONkaar). ओंकार can be written as ओँकार (ONnkaar).
As discussed earlier, the Om sound can be written as ओम in DevaNagari. So ॐ is a kind of short cut of the word ओम in DevaNagari and other Indic scripts.
People use this sign/symbol for meditation and worship.
Om symbol is drawn mostly as in the picture below i.e. as ॐ.
If you want a bigger picture of the Om symbol, click the above picture.
Is Om a religious symbol?
YES. It is main religious symbol for Hindus and Buddhists (Bauddh; बौद्ध). Sikhs have a derived form called एक ओंकार(Ek ONkaar).
In Hindi and Sanskrit, shape = AAkaar (आकार) or AAkRIti (आकृति) glyph = AkShar (अक्षर) or AkSharaakRiti (अक्षराकृति) indicate = saNket (संकेत) symbol = saNket + AkShar (संकेत-अक्षर) saNket + AkShar = saNketaakShar (संकेताक्षर) sign = chihna (चिह्न)
In Hindi dharma means religion. So it is mainly a religious symbol (dhaarmik chihn; धार्मिक चिह्न).
What is ओ३म् (O3m)?
Maharshi Dayanand Saraswati (महर्षि दयानन्द सरस्वती; maharShi dayaanand sarasvatee) was founder of the Arya Samaj. He used to write ओ३म् instead of ओम. The ३ (DevaNagari digit 3) between O and m is called ploot (प्लूत). Dayanand used ploot to emphasize long pronunciation of O. Only followers of Dayanand Saraswati (members of Arya Samaj) write ओ३म् instead of ॐ.
The syllable that is prior to a ploot is pronounced for a longer time/period (more than double). So ओ३म is to be pronounced as OOOm (o..m).
Is Om the most powerful symbol?
There is no scientific study to prove that ॐ is better or more powerful than any other symbol or letter for meditation etc. No symbol can really bring good luck, wealth or power. This symbol is sometimes misused by greedy preachers/god-man. How about using this symbol for peace!
Can Om symbol help you in meditation?
If a dark circle (or a point) can help you in meditation then the Om symbol will also help.
Proper Use of Om
Someone wrote that a reverse (flipped) Om brings bad luck. Luckily most Hindus do not believe in such nonsense. If you care for sentiments of Hindus (who are mostly peace-loving), avoid drawing this symbol on footwear, near dirty places, etc. If you want to make tattoos including this symbol, please try to maintain the shape and avoid tattooing it on leg, thigh, etc.