At one time in the past, the Lord of Great Compassion, the Noble Avalokiteshvara, raised the Idea of Enlightenment, bodhicitta, and then for countless kalpas (eons) accumulated merit. After passing through the ten Bodhisattva levels, he received the special Great Light empowerment.  Then, as he entered the ranks of the Noble Sons of the Buddha, he made this vow: 

"Throughout the samsaric world realms in the limitless space of the ten directions, I will benefit beings.  I must liberate all beings from samsara.  Not until all beings are established on the level of Buddhahood, not even one left behind in samsara, will I myself enter Buddhahood.  Only when all beings without exception have been guided to Buddhahood, will it be well for me to achieve it.  Until then I will remain in samsara for the benefit of all beings.  And to ensure it, may my body be shattered into a thousand pieces if I break this vow." 

From then on, Avalokiteshvara resided on Potala Mountain.  Through his limitless emanations, at every moment he accomplished the ripening and liberating of innumerable sentient beings -- to an extent beyond our means to express.  And in this manner he passed uncountable years -- many, many kalpas. 

About the name, Avalokiteshvara

The Sanskrit epithet Avalokiteshvara literally means Worldward-looking Lord.

It is transliterated into our alphabet from Tibetan:  phags-mchog spyan-ras-gzigs and, as Tibetan spelling is a bit like English in that letters have become silent or are pronounced in a surprising fashion, the phrase comes out P'hagpo Chenrezi.  (Often in respect of the Tibetan spelling, there is a final letter  -g or -k but it is not generally pronounced.)

Geshe Palden Dakpa explains that Chenrezi is the very embodiment of all compassionate motivation.   His activity takes many different physical forms including deities and other spiritual beings, teachers and helpers of all kinds including animals and even objects.

In the traditional manner, the Geshe breaks down the designation of this deity into its components: phags-mchog is Tibetan for noble, a lord (Skt: arya used in the way that Buddha Shakyamuni is said to have used the word - as meaning a person who is superior by virtue of rank plus: intelligent, skilled, aware, cultured and sophisticated, in comprehension of the human condition) but in addition, possessing the merit and compassion to en-noble others.  In other words, a bodhisattva.   Spyan-ras-gzigs - Chenrezig - "one who looks down with an unwavering eye" (an observer, scrutinizer, supervisor.)

A p'hagpa or noble is so by virtue of:
1. his or her basic state as compared to that of ordinary beings:  free of even the first link of the chain leading to becoming or the accumulation of karma 
2. the causes of the superiority: realizing the true Empty nature of existence
3. the unfolding of that superiority through the realization that there is no Self
(These are the 3 wisdoms: of hearing or study, of contemplation and of meditation.)

4. the intrinsic nature of a person who becomes superior:  As a consequence of the above realizations, this 'noble being' - a bodhisattva permanently free from rebirth in the 3 lower conditions - has the ability and desire to liberate others. 

Avalokiteshvara is considered a ' Buddha Jewel'; superior not only to ordinary beings, but to other superior beings. 

In the phrase spyan-ras-gzigs, Chenrezig, Looker- with- Unwavering-Eye, the verb to look is used in the sense of 'look after' like a mother who always and continuously tries to provide care, benefit and protection for her children.

Besides, 'looking after' all beings in this way, Chenrezi possesses "the five eyes and six super knowledges."  In other words, the 'looking' is done in 5 ways: 

His physical eye can see clearly over great distances, his divine eye refers to his ability to see past and future - birth, life and death of all - as well as the events in the present, his wisdom eye is the knowledge that all phenomena are empty of inherent existence, his Dharma eye is his ability to gauge the nature of the disciple's intelligence, and his Buddha Eye is his  " supreme and ultimate knowledge which directly knows all phenomena simultaneously".

" Avalokiteshvara's teaching goes on perpetually till the end of cyclic existence"  and since he has the supreme attributes of Buddha activity, he can appear in whatever forms best suit his disciples.   Some well-known forms are The Thousand- Armed and Thousand-Eyed, Eleven- Faced, Sinhanada and so forth.  Geshe Palden Dakpo says that the forms conform to the aspirations of specific disciples. 

The most usual is the four-armed form in which the white male human form is seated holding up a mala in his upper right hand, a lotus in the upper left and a jewel in his cupped hands. 

" His holding a white lotus flower in his second left hand symbolizes his stainless wisdom that has realized the nature of emptiness.  Just as the lotus blossom, although rooted in mud is not soiled by it, his pure wisdom is undefiled by the faults of the world." 

" His holding a crystal rosary in his second right hand symbolizes his liberating sentient beings from cyclic existence with ideal means and aspirations. "

"The jewel symbolizes Bodhichitta, the mind of enlightenment which is the treasure of supreme merits. His hands folded at the heart symbolize supplicating the Buddhas and Bodhisattvas of the ten directions, out of their great compassion, to look after poor bewildered beings. "

The deer skin draped over his left breast symbolizes his especially great attitude of  compassion towards all the suffering sentient beings. 

Avalokiteshvara's mantra is the famous one of six-syllables: 

"The syllables are:  Om-ma-ni-pad-me-hum. 

The first syllable OM represents the Form Body of a Buddha, and the last syllable HUM represents his Truth Body. 

MANI means wish-fulfilling gem symbolizing the pure Wisdom that has realized emptiness. 

Some people think that the vowel E ending the word PADME is a [vocative suffix which indicates the] form used to call to someone.  

[The mantra] is essentially a short symbolic supplication to [Chenrezi] saying:

'O, Supreme Avalokiteshvara, you have attained the two Bodies of a Buddha through the dual path of wisdom and method indicated by the jewel and lotus you hold, please lead all sentient beings to attain the two Bodies of Buddha as you have done!' "

~ edited from Geshe Palden Dakpa as translated by Karma Gelek Yuthok,  at Quiet Mountain

The case-ending -E can also indicate that the MANI belongs to the PADME or lotus which is the manifestation of Buddha-Nature in our realmie. Not "the jewel in the lotus" at all, but "the lotus' jewel." This jewel is the blue beryl, the Wish-fulfilling Chintamani.