You are that kutastha chaitanya (the immovable and changeless Consciousness) which is free from kartrutva (doership) and bhoktrutva (enjoyership), but you wrongly identify with the body-mind-sense complex and call it as ‘I’ and ‘mine’. This wrong identification is what is called adhyasa (superimposition) and this is the only ajnana (ignorance) in Vedanta. This adhyasa of the nature of mutual superimposition of atma (Self) and anatma (non-Self) is the sole cause of kartutva and bhoktruva.
The bodiless (asharira) suddha chaitanya (Pure Consciousness) is taken to be karta (doer) superimposing karmendriyas (organs of action) etc. onto it; imputing jnanedriyas (organs of knowledge), it is taken to be bhokta etc; superimposing the prana (vital force), it is taken to be in hunger, thirst etc, and due to the superimposition of antahkarana (inner organ) onto it, it is taken to be thinker, knower etc. So, the anatma and its characteristics are superimposed onto the atma and its characteristics (consciousness, existence) are superimposed onto the anatma.
Now, the question arises: where does this anatma come from? As we know, only two differently existing entities can get mixed up to share their properties. One is forced to accept this adhyasa in the form of mixing up of atma and anatma (however illogical it is) due to its presence in the anubhava (empirical experience) of all human beings. But, by accepting this, the presence of the anatma also gets accepted! This will pose real difficulty for the proponents of non-duality! According to Shankara, this is of the nature of satya-anrutam (Truth-untruth) mix up. This mix up is between one satya vastu (Object; substance) with that of another illusory one.
Atma, being really real, does not change (kutastha). It is of the nature of Consciousness which is self-evident and self-revealing. It is limitless and advitiya (non-dual). It is sajatiya, vijatiya, svagata bheda-rahita (free from generic, extrinsic, and Intrinsic differences)
So, atma mixing up with anything else is out of question. But still, it is said, atma mixes up with the anatma and thus forms the whole vyavahara (activity/dealing). And, this mix up is the cause of samsara (cycle of birth and death). What does this mean? To understand this, we will have to look into the nature of avidya.
So, what is the nature of this adhyasa – atasmin tatbuddhi (taking something other than what it is)! Ajnana is of the nature of error presenting something which is not present in the locus – seeing something which is not really present. This error, i.e. mithyajnanam (misaaprehension) is what is adhyasa / ajnanam. Now, if we apply this in the case of misunderstanding between atma-anatma, what boils down to is that the anatma is being superimposed onto the atma entirely due to an error. The vastu (substance, the truth) present is only atma but due to an error it is being seen as atma and anatma.
In susupti, there is only atma on whose substratum alone the whole set of dualities (‘I’-notion and the objective world) appears and disappears, and this is only from our natural erroneous standpoint of ajnanam. Just as a person with defective eye-sight sees the dual moon where only one exists, due to this brhantibuddhi (wrong understanding) the non-dual Brahman / atman appears as the multiplicity. And even while this appearance is present, the sole Reality, atman, is not the least affected thereby. And without forgoing its nature as the Pure Consciousness it illumines all the appearance. It is only from this standpoint of error that the atman is said to be saakshi (Witness) illumining the appearance.
It only means, the existence of anatma cannot be counted along with atma, the only Reality. That appearance, which we can locate only while in error, cannot be as existent even while it is present. Therefore, the anatma is mithya (illusory). Mithya is something which is not existent even while it appears. Because it appears only while one is subject to an error. Therefore, anatma is maya (illusion).
While one can dismiss anatma by calling it an illusion, shruti surpasses the common erroneous thought process. Another angle of illusion is rather more accurate to the shruti and anubhava. For instance, when one sees the snake superimposed on the rope, that ‘rope-snake’ is certainly illusory. It only means that the snake in reality does not exist even while one sees the snake superimposed on the rope. Nevertheless, one sees something, and that very vision of ‘something’ is not illusion. One cannot overlook this vision. So, in a way, it is wrong to say that what one saw was an ‘illusory snake’ or that there was no snake etc. But rather it is quite realistic to say that what one saw was rope only, which alone appeared as the snake due to the misconception. Applying this drastanta (illustration), the sole Reality, atma, is erroneously looked upon as the duality, but that Reality alone is what is present even right now, and ‘you are That’ only. Duality is just an erroneous perception caused solely due to misunderstanding (adhyasa). If it is asked, ‘whose perception it is’, it is the perception of the very questioner who is seeing. It means the misperception belongs to the ‘misperceiver’ while in error (i.e. adhyasa as pointed out already). There is no cause of ajnana; it is just naisargika (natural).
Again, all the pramana-prameya vyavahara (empirical activities where separate subjects and objects are perceived – physical-mental / laukika-vaidika) are based upon this error, viz. the dehatmabuddhi (body-identification). We cannot relate this adhyasa with time sequence as time etc. are also only within the ambit of adhyasa. So, the question ‘how did adhyasa happen’, and ‘what is the true mechanics of this adhyasa’ etc., is not tenable, and serves no purpose to the sadhaka. What is anubhava (experience) need not to be verified by anumana (inference), rather needs to be acknowledged as it is. Not recognizing this so obvious and unambiguous teaching of the shruti, our mind may be prone to seek the cause of this adhyasa, and for sure we can find some idea (erroneous though) to be the cause of this wrong comprehension.
Avyakrita-vyakrita, nama / roopa (unmanifest-manifest names and forms) were related only in adhyasa-avastha (in the state of superimposition). In the absence of adhyasa, the unmanifest is just an inference only with reference to the adhyasa standpoint. So, the Reality wrongly comprehended alone appears as the jagat, just as the rope wrongly comprehended appears as the snake. In the same way, the potentiality with reference to not-corrected notion of adhyasa-buddhi (wrong notion of superimposition) is maya. Therefore, Shankara has clearly stated in many ways that maya (nama/roopa etc.) is avidya-pratisthapita / avidya-krita / avidya-kalpita etc. Only if understood in this way, i.e. nama / roopa is avidya pratisthapita etc., and Brahman being the only Reality, one can, here and now, sublate the entire duality and can remain as the sole Reality of the present moment’s experience.