The opening verse of the Bhāgavata purāṇa 1.1.2 explains that there is a vastu or substance, which is to be understood by studying the Bhāgavata. This is also called the ‘tattva’ (lit. ‘that-ness’) in verse 1.2.11 which goes as follows:

vadanti tat tattva-vidas tattvaṁ yaj jñānam advayam
brahmeti paramātmeti bhagavān iti śabdyate

All those who have realized Absolute Reality refer to that reality as non-dual consciousness. This nondual consciousness is referred to as Brahman, Paramātmā and Bhagavān.

What do the words advaya-jñāna or nondual consciousness mean? Śrī Jīva Goswami explains this in Anuccheda 51 of the Tattva Sandarbha as follows:

jñānam=cid-eka-rūpam, or purely of the nature of consciousness.

The word jñānam in this verse does not mean ‘knowledge’ as misconstrued by many. The word ‘knowledge’ connotes information or content captured in a specific language, which is not the meaning intended here at all. Rather, Absolute reality is consciousness alone, which means it is completely devoid of any material (i.e. non-conscious) substance.

Further, Śrī Jīva explains that the word ‘advaya’ is used to qualify jñānam because of three reasons:

svayaṁ-siddha-tādṛśātādṛśa-tattvāntarābhāvāt: because there is no other Reality (tattva), either similar or dissimilar, that is self-existent;

śakty-eka-sahāyatvāt: because the nondual Absolute is supported only by its own inherent śaktis;

paramāśrayaṁ taṁ vinā tāsām asiddhatvāt: these śaktis can have no existence without it as their absolute foundation.

The Absolute Reality is not non-dual consciousness or advaya-jñāna because it alone exists. Rather all other substances that exist other than the Absolute Reality are utterly dependent on the Absolute Reality for their existence. Further, the Absolute Reality needs no external support for its own existence. It is in this sense alone that Absolute reality is advaya.

As an aside, there are three types of bheda or difference which must be absent for a substance to be considered ‘non-dual’. The substance in question should not have in it, the following types of divisions:

a) sajātīya bheda: a difference between objects of the same class. Here, ‘difference’ implies an independent existence.

b) vijātīya bheda: a difference between objects of different classes.

c) svagata bheda: a difference between an object and its parts.

Bhagavān, the Absolute Reality, does not have any of these bhedas in Him for the following reasons:

a) absence of sajātīya bheda: Members of Bhagavān’s class are His different forms such as Rāma, Balarāma, and so on. These expansions are not different in essence from Bhagavān – they are Bhagavān Himself but in a different mood. Naturally, these expansions of Bhagavān have no independent existence from Him.

b) absence of vijātīya bheda: The jīvas and prakṛti are both not in Bhagavān’s class, but they also have no independent existence from Him as they are His śaktis.

c) absence of svagata bheda: Bhagavān’s form appears as if it has limbs or parts in it, like the bodies of human beings. Each atom of each limb of the body has an independent existence from the body, it only temporarily appears to exist as if part of a single unit. But Bhagavān’s limbs are made of a conscious, uniform substance (viśuddha sattva), and are not separable from Him. Therefore they do not have an independent existence from each other, or from Bhagavan. Thus there is an absence of svagata-bheda in Bhagavān.

Summary

In the compound word advaya-jñāna, jnāna means pure consciousness, and advaya means nondual. Non-dual here specifically means that Bhagavān alone is self-existent, His śaktis have no independent existence of Him, and nothing exists other than Bhagavān and His śaktis. In other words, the purely conscious Bhagavān is the only independently existing entity.