First , some meanings, to put everything in context:
The word Yoga means a coming together, a joining up, a connection.Veda means knowledge, and antarefers to the end or perhaps, an ending.
So, looked at in the first way, as an end to the Veda, veda-anta refers to the concluding portions of the Vedas. These concluding portions are also called the Upanishads. The tradition holds that there are 14 principal Upanishads, each of which is an exposition of the truth as the rishis saw it. (the word rishi itself means ‘see-er’, the one who sees).
Looked at in another way veda-anta refers to the ending of knowledge. The word ‘knowledge’ in this context is not restricted to just the Veda, but refers instead to the ending of all kinds of knowledge, a statement that should, if one is awake to what has been written, immediately arouse curiosity.
Maha refers to something great, something immense. Vakya is a statement, a sentence. So a Mahavakyais a terse, profound statement of truth, something like Einstein’s equation: E = mc2.
These mahavakyas, of which the tradition says there are four, are presented in the Upanishads as the vision of the rishi. In this connection, it is important to realise that these mahavakyas were presented to the student by the guru, only after the completion of a long period of study and reflection, of sravana and manana, just as quantum physics, or relativity theory, for example, is taught only to advanced students.
प्रज्ञानम् ब्रह्म | Prajnanam Brahma Appearing in the Aitareya Upanishad , this statement refers to the insight of the rishi that Consciousness is Brahman
अयम् आत्मा ब्रह्म | Ayam Atma Brahma This statement, appearing in the Mandukya Upanishad of the Atharva Veda , reaffirms the identity of atman (a word that can very loosely be translated as soul) and Brahman. .
तत् त्वम् असि | Tat Tvam Asi This statement from Chandogya Upanishad of the Sama Veda once again affirms the supreme identity: one’s innermost self is not different from that which we call Brahman. .
अहम् ब्रह्म अस्मि | Aham Brahma Asmi This statement appears in the Brihadaranyaka Upanishad r . The meaning is that one’s self is not different from Brahman, the supreme reality.
It must be noted that the verbal translations of the Mahavakyas do not convey the sense of the realisation that that is embodied in these short statements. And most importantly, the ‘I’ referred to in these words is not the everyday, transactional ‘I’ that we refer to as the ‘ego’ but something else, which will be what we will explore in the days to come.