Om mani padme hum

is the six-syllabled Sanskrit mantra particularly associated with the four-armed Shadakshari form of Avalokiteshvara, the Bodhisattva of compassion. It first appeared in the Mahayana Kāraṇḍavyūha sūtra, where it is also referred to as the sadaksara and the paramahrdaya, or "innermost heart" of Avalokiteshvara. In this text, the mantra is seen as the condensed form of all Buddhist teachings.
The precise meaning and significance of the words remain much discussed by Buddhist scholars. The literal meaning in English has been expressed as "praise to the jewel in the lotus", or as a declarative aspiration, possibly meaning "I in the jewel-lotus". Padma is the Sanskrit for the Indian lotus and mani for "jewel", as in a type of spiritual "jewel" widely referred to in Buddhism. The first word, aum/om, is a sacred syllable in various Indian religions, and hum represents the spirit of enlightenment.
In Tibetan Buddhism, this is the most ubiquitous mantra and its recitation is a popular form of religious practice, performed by laypersons and monastics alike. It is also an ever-present feature of the landscape, commonly carved onto rocks, known as mani stones, painted into the sides of hills, or else it is written on prayer flags and prayer wheels.
In Chinese Buddhism, the mantra is mainly associated with the Bodhisattva Guanyin, who is the East Asian manifestation of Avalokiteshvara. The recitation of the mantra remains widely practiced by both monastics and laypeople, and it plays a key role as part of the standard liturgy utilized in many of the most common Chinese Buddhist rituals performed in monasteries. It is common for the Chinese hanzi transliteration of the mantra to be painted on walls and entrances in Chinese Buddhist temples, as well as stitched into the fabric of particular ritual adornments used in certain rituals.
The mantra has also been adapted into Chinese Taoism.

Meaning and effects

Semantic

s may be interpreted by practitioners in many ways, or even as mere sequences of sound whose effects lie beyond strict semantic meaning.
The middle part of the mantra, ', is often interpreted as being in the locative case, "wish-fulfilling jewel in the lotus", Sanskrit ' "wish-fulfilling/priceless gem, jewel, cintamani" and the locative of ' "lotus". The lotus is a symbol present throughout Indian religion, signifying purity and spiritual fruition. Maṇipadme is preceded by the ' syllable and followed by the ' syllable, both interjections without linguistic meaning, but widely known as divine sounds.
However, according to Donald Lopez it is much more likely that ' is in fact a noun of address, addressing in the vocative case a Bodhisattva called ', "jewel-lotus" – an alternative epithet of the Bodhisattva Avalokitesvara.
Damien Keown also notes that another theory about the meaning of the mantra is that it actually invokes a female deity named Manipadmi. This is due to evidence from texts such as the Kāraṇḍavyūhasūtra which depict the mantra as a female deity. Also, as noted by Studholme, if the word is read as a noun of address, it is most likely in the feminine grammatical gender, because if masculine, it would be a highly irregular form. Thus as Lopez notes, the original meaning of the mantra could in fact be an invocation of "she of the lotus jewel", who is the vidya and consort of Avalokiteshvara and is equivalent to Shakti's role vis a vis Shiva.
Regarding the relationship between the jewel and the lotus, Sten Konow argued that it could either refer to "a lotus that is a jewel" or to "a jewel in the lotus". He argues that the second explanation makes more sense, indicating Shaivite influence through the imagery of the lingam and the yoni, both also terms associated with mani and padma respectively. Thus the mantra could in fact mean "O, she with the jewel in her lotus".
According to Alexander Studholme however, the meaning of manipadme "should be parsed as a tatpurusa, or 'determinative', compound in the locative case", meaning "in the jewel-lotus", or "in the lotus made of jewels", which refers to:

the manner in which buddhas and Bodhisattvas are said to be seated in these marvelous blooms and, in particular, to the manner in which more mundane beings are believed to appear in the pure land of the buddhas. Given the predominance, in the Kāraṇḍavyūha and in the Mahayana in general, of the religious goal of the pure land of Amitabha, it may be safely assumed that ' would have been quite naturally associated with the mode of the rebirth of human beings there. The recitation of, then, the bringing to mind of the name of the Buddhist isvara, includes a declaration of the manner in which a person is reborn in Sukhavati: "in the jewel lotus."

According to the ''Kāraṇḍavyūhasūtra''

The first known description of the mantra appears in the Kāraṇḍavyūha Sūtra, which is part of certain Mahayana canons such as Chinese and Tibetan. In this sutra, Shakyamuni Buddha states, "This is the most beneficial mantra. Even I made this aspiration to all the million Buddhas and subsequently received this teaching from Buddha Amitabha."
The sutra promotes the recitation of this mantra as a means to liberation. It states that whoever knows the mantra will know liberation as a fully enlightened Buddha. It also states that initiation into the mantra by a qualified preceptor is an important requirement for practicing this mantra. In the sutra, Avalokitesvara says that the mantra should not be given to one who has not seen the mandala. This initiation is said to be open to all Buddhists regardless of class and gender, whether they be of the Mahayana or Hinayana, but not to tirthikas.
The Kāraṇḍavyūhasūtra also sees the mantra as the pith or condensed expression of all "eighty four thousand Dharmas". Because of this it is called "the grain of rice of the Mahayana", and reciting it is equivalent to reciting numerous sutras.
Thus, according to Studholme, the significance of the mantra in the Kāraṇḍavyūha is mainly that it is the "innermost heart" of Avalokitesvara, and therefore is "a means both of entering into the presence of Avalokitesvara and of appropriating some of the Bodhisattva's power". Its practice is said to lead numerous positive qualities including:

The seeing the Bodhisattva's "thousand-fold" form,
Rebirth into the myriad worlds contained in the pores of the Bodhisattva's body
Innumerable samadhis, including the samadhi of "rejoicing in loving kindness and compassion".
The development of "great compassion"
Accumulation of immeasurable merit
Accomplishment of the six perfections
Awakening

In this sutra, the sadaksari mahavidya also appears as a goddess, "autumn yellow" in color, with four arms, with two arms holding a lotus and prayer beads, and the other two in anjali mudra. According to Studholme, these features are similar to the way the mantra Om nama shivaya is depicted in Shaiva texts, since "both are concise vidyas, the hrdayas of their respective isvaras, sui generis means of attaining liberation, universally available, though of rare value and somewhat secret. Both are also, it has been argued, conceived of as forms of pranava ."

In Tibetan Buddhism

The 11th-century Bengali master Atiśa Dīpaṃkara Śrījñāna, who was influential in bringing Buddhism to Tibet, also wrote a short treatise on the mantra called the Arya-sad-aksari-sadhana. Some Buddhist scholars argue that the mantra as practiced in Tibetan Buddhism was based on the Sadhanamala, a collection of sadhana or spiritual practices published in the 12th century. However, according to Peter Alan Roberts, "the primary source for Tibetan Avalokitesvara practices and teachings" is the 11th-century Maṇi Kambum.
Donald Lopez writes that according to a 17th-century work by the prime minister of the fifth Dalai Lama, the meaning of the mantra is said to be "O, you who have the jewel and the lotus." That manipadme is a noun of address is also supported by a 9th-century Tibetan grammatical treatise.
Lopez also notes that the majority of Tibetan Buddhist texts have regarded the translation of the mantra as secondary, focusing instead on the correspondence of the six syllables of the mantra to various other groupings of six in the Buddhist tradition.
For example, in the Chenrezig Sadhana, Tsangsar Tulku Rinpoche expands upon the mantra's meaning, taking its six syllables to represent the purification of the six realms of existence:

Syllable	Six Pāramitās	Purifies	Samsaric realm	Colors	Symbol of the Deity	To be born in
Om	Generosity	Pride / Ego	Devas	White	Wisdom	Perfect Realm of Potala
Ma	Ethics	Jealousy / Lust for entertainment	Asuras	Green	Compassion	Perfect Realm of Potala
Ni	Patience	Passion / desire	Humans	Yellow	Body, speech, mind quality and activity	Dewachen
Pad	Diligence	Ignorance / prejudice	Animals	Blue	Equanimity	the presence of Protector
Me	Renunciation	Greed / possessiveness	Pretas	Red	Bliss	Perfect Realm of Potala
Hum	Wisdom	Aggression / hatred	Naraka	Black	Quality of Compassion	the presence of the Lotus Throne

According to Trijang Rinpoche

The tutor to the present Dalai Lama, Trijang Rinpoche wrote a commentary on the mantra which states:

Regarding mani padme, "Jewel Lotus" or "Lotus Jewel" is one of the names of the noble Avalokitesvara. The reason that he is called by that is that, just as a lotus is not soiled by mud, so the noble Avalokitesvara himself has, through his great wisdom, abandoned the root of samsara, all the stains of the conception of true existence together with its latencies. Therefore, to symbolize that he does not abide in the extreme of mundane existence, he holds a white lotus in his hand...He joins the palms of his two upper hands, making the gesture of holding a jewel to symbolize that, like a wish-granting jewel, he eliminates all the oppression of suffering for all sentient beings and bestows upon them all temporary and ultimate benefit and bliss.