What is meant by Brahman as Nirguna, sachchidanada or sat-cit-ananda ontologically, according to Adi Samkara?

The supreme reality Brahman (God including the names Visnu, Siva et al) as Nirguna (meaning unattributed) is best described by Sachchidananda (sat cit ananda)*. Samkara does not start, as theological philosophers do, with a discussion about Brahman having attributes. He is indifferent, and even critical of, the arguments which are adduced in favor of a great First Cause and Creator of the world. For him integral experience, or anubhava, is the basal fact. It is the highest religious insight. It supplies the proof 'if proof be the name for it' of man's awareness of a spiritual reality. Brahman is present to every man and is the universal fact of life. If any logical proof were necessary, Samkara points to the inability of the mind to rest in the realtive, i.e. the impossibility of accounting for experience except on the hypothesis of Brahman.

In his account of causality Samkara makes the causal nature the svabhava, or the samanya or the universal, while the effect is regarded as a condition, avastha, or visesa (particular). There are in the world many samanyas with their visesas -- both conscious and unconscious. All these samanyas in their graduated series are included and comprehended in one great samanya, i.e. in Brahman's nature as a mass of intelligence. To understand the nature of this universal reality is to know all the particulars involved in it.

To say that Brahman is reality is to say that it is different from the phenomenal, the spatial, the temporal and the sensible. Brahman is what is assumed as foundational, though it is in no sense substance. It is not in any point of space, though it may be said to be everywhere, since all things imply and depend on it. Since it is not a thing, it cannot have spatial relations to anything else, and is therefore nowhere. It is not a cause, for that would be to introduce time relations. Its nature is inexpressible, for when we say anything of it we make it into a particular thing. We may speak about it, though we cannot describe it adequately or have any logical knowledge of it. If the finite man can comprehend Brahman, then either our understanding must be infinite or Brahman finite.

Every word employed to denote a thing denotes that thing as associated with a certain genus, or act, or quality, or mode of relation. Brahman has no genus, possesses no qualities, does not act, and is related to nothing else. It is devoid of anything of a like kind or of a different kind, and has no internal variety. A tree, for example, has the internal variety of leaves, flowers and fruits, has the relation of likeness of other trees and of unlikeness to objects of a different kind like stones. Brahman has nothing similar to it, nothing different from it, and no internal differentiation, since all these are empirical distinctions. As it is opposed to all empirical existence, it is given to us as the negative of everything that is positively known. Samkara declines to characterize it even as one except in the sense of secondless, but calls it non-dual, advaitam. It is the "wholly other," but not non-being. We can at best say what Brahman is not, and not what it is. It transcends the opposition of permanence and change, whole and part, relative and absolute, finite and infinite, which are all based on the oppositions of experience.

When the Absolute is said to be Nirguna, this only means that it is trans-empirical, since gunas are products of prakrti and the Absolute is superior to it. The gunas qualify the objective as such, and God is not an object. The objects come and go, but the real persists as the permanent in the midst of all changes. So, it transcends the gunas or phenomenal being. The Absolute is not on that account to be regarded as mere blank. So, the Upanisad says "nirguno guni."

Brahman is of the nature of ultimate consciousness,  with knowledge as essence and not its property. It is not eternal in the sense of persisting changelessly through time, but in the sense of absolute timelessness and incorruptibility. It is eternal because its completeness and perfection are unrelated to time. The sequence which binds things and events in the time order has no meaning for it. It is eternal per durance, to which all time relations are irrelevant. It can only be negatively described as the other of its own otherness. It is sat (real), meaning that it is not asat (unreal). It is cit (consciousness), meaning that it is not acit (unconsciousness). It is ananda (bliss), meaning that it is not of the nature of pain (duhkha-svarupa). It is real, having authentic being. It never fails to be, since it depends on nothing to preserve it in being. It does not take in anything from outside itself, for then being would include non-being. There is no first or last in it. It does not unfold, express, develop, manifest, grow and change, for it is self-identical throughout. It cannot be regarded as a whole including parts, for it is uniform in nature (ekarasa). It is real and yet devoid of the nature of the world. Such a being cannot of course be physical, and quantitative and fragmentary. The everlasting being devoid of any deficiency is of the nature of consciousness, cit. Such a fullness of authentic being and ideality perforce is free delight, ananda. All human bliss is a phase of the bliss of Brahman. It is highest truth, perfect being and fullest freedom.

While Brahman is devoid of attributes, still those of being, consciousness and bliss may be said to be its essential features (svarupa-lakshanas), while those of creatorship, etc., are accidental ones (tatastha-lakshanas). Samkara knows that even the definition of Brahman as saccidananda or sat-cit-ananda (reality-consciousness-bliss) is imperfect though it expresses the reality in the best way possible. Vidya gives the highest positive conceptual account of Brahman by equating it with the attributes of being (sat), consciousness (cit) and bliss (ananda), which are self-sufficient. Avidya, or lower knowledge, applies attributes which imply relation, such as creatorship and rulership of the universe. These are thus two views of the ultimate, higher and lower. Where, by discarding the differences of name, form, and the like, ascribed by Avidya, Brahman is indicated by negative expressions, as not gross, etc., it is the higher (param). But where, on the contrary, exactly the reality is described, for purposes of worship, as distinguished by some difference or other, it is lower (aparam). Commenting on the spatial conception of Brahman, Samkara says that it is meant to convey our ideas to others or serve the purposes of worship. We rise to the highest in itself, Brahman, through the highest in relation to us or Isvara, the creator and Governor of the universe; we are obliged to think Brahman in worship as 'om tat sat' (creator, governor, true).

*Ref.:  Subhash C. Sharma, "Not everyone and everything is same or equal to Brahman (God) in Advaita: Brahman according to Samkara's Advaita," (April 22, 2004: "Brahman" @ Hindunet.com), Aug. 3, 2009,  http://web.archive.org/web/20091016215801/http://geocities.com/lamberdar/brahman_absolute.html

Brahman in essence as Nirguna is Sat-Cit-Ananda (explained in the above), whereas for the purpose of worship as Isvara (in Saguna depiction) according to Om-Tat-Sat (the Bhagavad Gita: Ch. 17 - V. 23-26).