In plain words
"'When it has set and waned through Jñāna, O Rāghava': when this avidyā has waned and perished, you will be able to know how it arose, how it grew and how it perished," Vasiṣṭha told Rāghava.
There is a secret in this teaching. As for where this world comes from and how it came to be, that is never resolved, even after ages upon ages of inquiry! If, by some vidyā, this could be shown to have come from somewhere, inquiry would bear a result; but the world is not such a matter. The question of how the world arose is the same as the question of how the snake arose in the illusion of a rope mistaken for a snake. What is actually there is a rope; yet from that, a snake arose. The cause of this snake's arising is the defect that resides in that viewer's intellect — that is, delusion, or ignorance. Therefore, the logical answer stands proven: the snake's manifestation is caused by ignorance. In just the same way, Brahman occupies the place of the rope, and the world occupies the place of the snake — that is, it is Brahman itself that we, out of delusion, take to be the world, and deal with as such. Here too one cannot but call it a defect in the Buddhi of the one who sees.
That is to say, seeing one object as another is clearly a defect of the intellect. Therefore this world may be determined to be a matter that has originated from a defect of the intellect. A matter born of such a defect of the intellect, born of delusion, can never, at any time, be true. When the delusion perishes, what was born of it perishes too, and the reality becomes apparent. This is the essence of Vedānta.