Neti Neti - The divine is not this, not that

Origin of Neti Neti and Translation

In Brhadaranyaka Upanishad, Yajnavalkya is questioned by his students to describe God. He states "The Divine is not this and it is not that"  (neti, neti).

Sanskrit Shloka:-
तत्त्वमस्यादिवाक्येन स्वात्मा हि प्रतिपादितः ।
नेति नेति श्रुतिर्ब्रूयादनृतं पाञ्चभौतिकम् ॥ २५॥ (Avadhuta Gita 1.25)

English Transliteration:-
tattvamasyādivākyena svātmā hi pratipāditaḥ ।
neti neti śrutirbrūyādanṛtaṁ pāñcabhautikam ॥ 25 ॥

"The Divine is not this and it is not that" (neti, neti).
Neti or नेति = न + इति means "not this, not this" that is beyond description. 

Vedantic Neti Neti as explained by Adi Shankara

Adi Shankara was one of the foremost Advaita philosophers who advocated the neti-neti approach. In his commentary on Gaudapada’s Karika, he explains that Brahman is free from adjuncts and the function of neti neti is to remove the obstructions produced by ignorance. His disciple, Sureshvara, further explains that the negation, neti neti, does not have negation as its purpose, it purports identity (Harold G. Coward. Negative Theory. SUNY Press. p. 204).  

The sage of the Brihadaranyaka Upanishad II iii 1-6, beginning with there are two forms of Brahman, the material and the immaterial, the solid and the fluid, the Sat ‘being’ and tya, ‘that’ of Satya – which means true, denies the existence of everything other than Brahman. And therefore, there exists no separate entity like Jiva which Shankara states is the reflection of Brahman in Avidya or ignorance (Baman Das Basu. The Sacred Books of the Hindus Vol.5, Part 1. Genesis Publishing Private Ltd. p. 480).

Neti Neti According to Yogopedia

In Jnana yoga and Advaita Vedanta, "neti-neti” may be a chant or mantra. It is an 8,000-year-old practice that takes the focus away from all disturbances, so the practitioner may find the stillness in every movement and the formless in every form. Neti-neti meditation helps to identify all things of the world which are not the atman (the real), thus negating the anatman (the unreal).

When it's adapted for the modern world, including neti-neti meditation in one's yoga practice, neti-neti helps the practitioner realize that they are not actually the things that they normally identify themselves with (personalities, thoughts, feelings or jobs), nor are they merely their roles (parents, partners, friends or siblings) in life. In this way, neti-neti can also be interpreted as "beyond this, beyond that."

Self versus Non-self

Neti neti is a keynote method of Vedic inquiry of oneness through negation.  With the use of this method the wise one (gyani/nani) negates identification with all things of this world which is not the Atman (self or soul), in this way he negates the Anatman (non-self). Through this gradual process the wise one negates the mind and transcends all worldly experiences that are negated till nothing remains but the Self. According to Vishnu Devanand in Meditation and Mantras: An Authoritative Text: "Through this process the wise one attains union with the Absolute by denying the body, name, form, intellect, senses and all limiting adjuncts and discovers what remains, the true "I" alone." This is the true yog, or union (yog - junction). 

Guru Arjan on Neti Neti

Guru Arjan Dev mentions this concept in his Salok Sehshritee on page 1359 of the Guru Granth Sahib.

न संखं न चक्रं न गदा न सिआमं ॥
अस्चरज रूपं रहंत जनमं ॥ 
नेत नेत कथंति बेदा ॥ 
ऊच मूच अपार गोबिंदह ॥ 
बसंति साध रिदयं अचुत 
बुझंति नानक बडभागीअह ॥५७॥ 

God has no conch-shell, no religious mark, no paraphernalia; he does not have blue skin.
His Form is Wondrous and Amazing. He is beyond incarnation.
The Vedas say that He is not this, and not that.
The Lord of the Universe is Lofty and High, Great and Infinite.
The Imperishable Lord abides in the hearts of the Holy. 
He is understood, O Nanak, by those who are very fortunate. ||57|| 

Net Net Reflected in Guru Nanak's Mool Mantra

Neti Neti Reflected in Bulleh Shah's poetry

Bulleya Ki jaana main Kaun
Bulleya who knows who I am

Na main momin vich maseetaan
Na main vich kufar diyan reetaan
Na main paakaan vich paleetaan
Na main moosa na firown 

Not a believer inside the mosque, am I
Nor a pagan disciple of false rites
Not the pure amongst the impure
Neither Moses, nor the Pharoh 

Neti Neti: A story from the Shiv Purana

Brahma really wanted to describe everything that he knew for those who didn't understand.  He wanted to say and document everything in the vedas.  He desired to not just describe everything in the world, but everything that the world comes from. 

He came to a congregation of holy men, "devtaas".  His one condition was that he would only give his wisdom to ones who were ready to receive it. He was looking for listeners. If there were no listeners, he would not speak.  

One day he complained that he was not going to speak.  When Shiv asked him why that was, he said there were no listeners. All these folks only listened to their own desires. They were all mired in the conflicts of their minds.  

Brahma complained that there were only two listeners in this whole congregation -- Shiv and Vishnu.  And he didn't really want to tell them anything, because they already knew everything he had to tell. They knew about beauty, about divinity, about longing, about love, about purity, about knowledge. Shiv and Vishnu already knew everything he knew.  Brahma wanted to know that as well.  Vishnu blessed him that he would be successful. But Shiv didn't bless him.  He said I will bless you only when he himself knew everything.

After years of giving his wisdom, he said he was going to end his lectures.  I won't say with words. He said "Neti Neti."  Brahma ended the vedas with "Neti Neti."  Whatever I have said is not is not. My words are incomplete.  Then Shiv said, now that you understand that you are incomplete, you are complete.  The ocean does not have to say that I am the ocean.