What does avidya or ignorance mean in the context of the 12-nidânas (links). Well, that is an interesting question. Buddhists are all familiar with the 12-nidânas beginning with ignorance, followed by karmic impressions (samskâra), consciousness, subject-object, the sense organs, sense contact, sense experience, thirst, mental clinging, becoming, birth, old age and death.
In his translation of the Madhyanta-vibhanga, Th. Stcherbatsky renders avidya with "transcendental illusion." Here is a snip of the meaty part.
Now this gets interesting. Avidya as the transcendental illusion is the a priori and necessary condition for human rebirth. With vidya, on the other hand, no rebirth is possible. Ultimate reality is disclosed to us. The former covering by which true reality was hidden from us such that we were tormented, is removed. We have obtained absolute knowledge by beholding the substance of the illusion. The transcendental magic trick has come to an end.
Before our gnosis or knowledge of the absolute, we were trapped in something like a circle of illusion which for us seemed inescapable. It is something like a Mandelbrot fractal which is an infinitely changing phenomenal pattern that, at the same time, is self-limiting or bounded. It is Hegel's bad infinite which is not encompassable. We can't get out of it, in other words. Truth be told, only gnosis of the absolute substance can encompass this bad infinite and thus conquer it. Not surprising, science admits that it does not know what the substance of the universe is! In is content to play in the fractal world of avidya, unable to encompass it.