Non-dual consciousness is known as nirvikalpa samadhi in Hinduism. Vikalpa means imagination or thinking, which is the main function of the mind. Thought or imagination implies duality, such as subject and object. Nirvikalpa means free of imagination and thinking and of dualistic consciousness in general. So “Nirvikalpa Samadhi” means an exclusive concentration upon the one entity without the distinct and separate consciousness of the knower, the known and the knowing, and without even self consciousness.
Non-dualist Vedantins, such as Shankaracharya and his followers, believed that Brahman (Reality), being non-dualistic in nature, can be grasped in such thought free concentration.
“The truth, that is Brahman, is surely realized by nirvikalpaka Samadhi, not by any other method. Otherwise, due to the inconsistency of the mind, it will be mixed up with other modifications.” (Vivekachudamani, verse 366).
Adi Shankaracharya says in another work that the salt mixed in water appears as water and does not appear as separate from water. Similarly, when the mind merges into Brahman, in manifests only as Brahman. This state concentration is called nirvikalpaka because there are no dualistic ideas in it.
He contends that by this Samadhi there arises the destruction of the knots of past impressions and of all karmas. There will be manifestation without effort of one’s nature, inside out and forever (Vivekachudamani 364)
The term is sometimes likened to the super reflective concentration of Yoga system of Patanjali. Though the term has affinities with these concepts, it seems to have emerged specifically in the tradition of the non-dualist Vedanta.