In plain words
"'I am ignorant' —" each of us, for himself, cannot but admit this. That is, conforming to the doctrine of the scriptures and examining the matter: the very one who, while being Brahman itself, does not know this to be so and thinks 'I am a jīva' — it has come to be known that this 'I myself' is the ignorant one. But then, is it possible to forget oneself and think of oneself as other? To remove that doubt, we have already learned many things.
Whoever is possessed of a false outlook — his being ignorant is reasonable. This delusion rests upon, and takes hold of, a person's mind. By its power one forgets one's own true nature, that is, one's ānanda-svarūpa, and is deluded into thinking oneself a jīva, believing happiness lies elsewhere, and so falls into saṃsāra and wanders about endlessly. Of such a one, śruti teaches: 'Seek out the Ātma, know it, and be blessed.'
Advaita's teaching does not, in fact, proceed by first proving that ignorance is a real, existing thing and then rejecting it. The very intellect that says 'I have no happiness,' 'This is what I need,' 'That I must attain and experience' — that Buddhi itself is jīvatva. Such an intellect is what they call ignorance. Therefore, if jīvatva is to perish, this intellect must transform itself into the understanding 'I am of the nature of bliss, one whose every desire is fulfilled.' The former notion is called ignorance, and the second notion is called Jñāna — that is, the intellect that holds the notion of jīvatva is ignorance, and the intellect that holds 'I am of the nature of bliss' is Jñāna. Heaping upon his own head troubles that do not even exist, thrashing about, struggling, dying and being born again, insisting 'I was in bondage' — to free the jīva who struggles on so, from such ignorance, the Advaita śrutis arose in order to define the matter thus: 'It is only your thinking so that is ignorance, mind you!' — and thereby to bring about true Jñāna. When we think ourselves 'the imprisoned,' it is we ourselves who are ignorant. In reality, we have not been created by anything, nor were we made into beings of little knowledge. To think that there is such a thing as this world, among the enjoyable things found within it,