"[I am] the nature of Pure Consciousness. I am always the same to beings, one alone; [I am] the highest Brahman, which, like the sky, is all-pervading, imperishable, auspicious, uninterrupted, undivided and devoid of action. I do not belong to anything since I am free from attachment. [I am] the highest Brahman... ever-shining, unborn, one alone, imperishable, stainless, all-pervading, and nondual-That am I, and I am forever released." - Shankara, The Upadesasahasri
Atman (or paramätman, the highest Self), for Advaita Vedanta is that pure, undifferentiated self-shinning consciousness, timeless, spaceless, and unthinkable, that is not different from Brahman and that underlies and supports the individual human person.
Ätman is pure, undifferentiated, self-shinning consciousness: It is a supreme power of awareness, transcendent to ordinary sensemental consciousness, aware only of the Oneness of being.
Atman is that state of conscious human being wherein the division of subject and object, which characterize ordinary consciousness, are overcome. Nothing can condition this transcendental state of consciousness: among those who have realized it, no doubts about it can arise. Atman is thus void of differentiation, but for Advaita it is not simply a void: it is the infinite richness of spiritual being.
Source: Advaita Vedanta : A Philosophical Reconstruction, Pages: 48