Adhyas, or illusion, means seeing what is not there. Shankara loved this word very much and for the Upanishads it is very fundamental. Adhyas means projection, seeing what is not there: what is seen is not really there, you are projecting it from within. You are the cause of the projection.
This world is not as you see it. It is dependent on you. If you change, the world also changes. A young man sees one world, an old man sees another, and children see yet another. What makes the differences? The world is the same. But the children do not have the same eyes that the young man has. Children are still interested in collecting stones and pebbles. Just the colorfulness of things is enough. The young man says, "Throw them away! What is in them? What value do they have?" For a young man money has become valuable. He has started understanding the value of money. Now collecting stones and pebbles won't do. Now it is no use running after butterflies.
Children are catching butterflies, they look heavenly to them. The young man takes children to be ignorant but when the man becomes old, his senses get tired, his experiences turn pungent and bitter and he feels as if his mouth is full of a kind of tastelessness. Now even young people appear like children to this man. For him, young people are running after different kinds of butterflies. Only the kind of butterflies has changed, but not the butterflies as such. Old people go on saying, explaining, that these are butterflies, but no young man listens to them. They themselves had not listened to their fathers and grandfathers. There is a reason for not listening, and that is that they have different eyes. If the young man receives the eyes of an old man he will see the same. And remember, the interesting thing is that if the old man can receive the eyes of the young again, he will forget all these experiences; he will forget all this wisdom he is displaying; the world once again will become colorful to him.
Shankara has divided reality in three categories, and those categories are beautiful to understand.
One category is the category of the truth: that which is. In fact nothing else is possible; only truth is and only truth can be.
The second category is of that which is untruth, which cannot be. No possibility of its being there, because how can untruth be? For being, truth is needed. So untruth is non-being, truth is being. Then Shankara finds a third category that he calls dreaming, appearance, illusion, maya: that which appears to be but is not.
So three categories. Truth, that which is. If your eyes are clear, unclouded, if the mind is not dreaming, then there is only one category -- truth. But if your mind is dreaming then two other categories come into existence.
Dream IS, in a certain sense, because you dream it. And it is not, in a different certain sense, because it corresponds to no reality. You dream in the night that you have become a king. In the morning you find you are just the same beggar. The dream was false, but the dream was, so it HAS a quality of truth about it because it happened. And in those moments when it was happening you completely believed in its truth, otherwise it would have stopped immediately.
If you become aware that "I am dreaming and this is false," the dream is broken, you are awake already. The dream existed for a few hours; it had one quality of truth, that it existed. But it is not true because in the morning you find it was not. It was just a thought, a wave in the air, a flower in the sky -- appeared to be true but was untrue.
Truth is being, untruth is non-being, and between the two there is a world of dreaming -- it carries the qualities of both. And mind is the source of dreaming, so mind IS illusory. Mind is the source of all MAYA.