In Advaita Vedanta, Adhyasa means a false superimposition of the characteristics of physical body (birth, death, skin color etc.)
The first mention of Adhyasa is found within the Brahma Sutra Bhasya of Adi Shankara.
Adi Shankara begins his commentary of the Brahma Sutras by explaining what Adhyasa is and its nature.
In his introduction to the commentary on Brahma Sutras, Shankara gives a definition of Adhyasa as thus - आह कोऽयमध्यासो नामेति। उच्यते स्मृतिरूपः परत्र पूर्वदृष्टावभासः। तं केचित् अन्यत्रान्यधर्माध्यास इति वदन्ति। केचित्तु यत्र यदध्यासः तद्विवेकाग्रहनिबन्धनो भ्रम इति। अन्ये तु यत्र यदध्यासः तस्यैव विपरीतधर्मत्वकल्पनामाचक्षते। सर्वथापि तु अन्यस्यान्यधर्मावभासतां न व्यभिचरति। तथा च लोकेऽनुभवः शुक्तिका हि रजतवदवभासते एकश्चन्द्रः सद्वितीयवदिति।।Swami Gambhirananda translates it as - If it be asked, "What is it that is called Superimposition?
"- the answer is - "It is awareness, similar in nature to memory, that arises on a foreign (different) location as a result of some past experience.