The term 'adhyaroopa' is used to express the nature of 'super imposition of the unreal on the real, like the serpent on the rope. The true nature of this objective world and our own existence in it has been discussed earlier. "Is this world real"? The answer is simply a 'no'. It is 'illusory', at best, a make-believe world that comes within the grip of time ('kaal'), space ('desh), and cause and effect ('karya-karana'). Nothing is permanent, unchanging, and eternal here. But, the beauty of this creation is such that, "sat covers the asad". This is akin to the spiritual aspect of 'Paramatman' that exists as the 'Atman in the gross ignorant physical body!
In fact, the entire universe is an ever-expanding one. It appears as if it is just galaxies, stars and planets! But is so vast expansive one that not much is known about it so far! There is a thin veil of physical space called Akasha that exists in the background of an invisible vast screen (brahmn). This veiling is the superimposition, adhyaroopa, of the visible world. This is "the apparent recognition of something previously observed in some other thing". This is like silver in the ochre of a shell or mother-of-pearl or water in a mirage.
Each and every object is moving away from each other, and the nature of human existence is no different! Thus, one can say, at best, this world appears as though it is real (in one perspective). This led Sri Madhvacharya of Udupi to expound the 'dvaita' concept. What is one, undivided, 'advait' appears as divided. Everything is Brahmn- sarvam khaluvidam brahmaa'! Brahmn is like the one Sun reflected by the several sheets of waves! The Vedic Texts describe this entire universe as one single and indivisible (avicChinna and abhedya) unit. The appearance of duality or multiple units of the One as many is due to the enveloping ignorance over the underlying true nature of the brahmn. This is like the pure crystal that appears like a colored one due to the color of the flower that covers it. This is akin to the pure Atman covered by the gross body in us.
Brahmn is the only real, the sat. All other that we see, hear, know, or perceive is an illusion, myth. Reality is Brahman. Existence (sat), Consciousness (chit), Bliss (Ananda), sat-chit-anandam brahma. Al other things are unreal, nescience, material objects that are subject to deterioration and discard. Brahman is the only basis, the Real, on which the asad, the Unreal, transient, mystical exists (in time and space).
'Brahman' is tat sat, tyat. The maha mantra is tat brahma, tat vishnu, tat sarvam. Brahman is One, without a second- Ekam adviteeyam.
One should refer to the Mandukya and Mundaka Upanishads in order to clearly understand the concept of duality and the nature of Brahmn. What is 'advait' about this world of multiple layers of nature? It is simply one individual only is a family, a community, society, nation and the world. This world of multifarious life-forms is one family- vasudhaiva kutumbakam is the Vedic doctrine. This calls for a more sensible way of human attitude and behavior- one of universal love, mutual respect, compassion, and sacrifice- one for all and all for one.