The Mahavakyas (sing.: mahāvākyam, महावाक्यम्; plural: mahāvākyāni, महावाक्यानि) are "The Great Sayings" of the Upanishads, as characterized by the Advaita school of Vedanta. Most commonly, Mahavakyas are considered four in number,
They all express the insight that the individual self (jiva) which appears as a separate existence, is in essence (atman) part and manifestation of the whole (Brahman).
Though there are many Mahavakyas, four of them, one from each of the four Vedas, are often mentioned as "the Mahavakyas". According to the Vedanta-tradition, the subject matter and the essence of all Upanishads are the same, and all the Upanishadic Mahavakyas express this one universal message in the form of terse and concise statements. In later Sanskrit usage, the term mahāvākya came to mean "discourse", and specifically, discourse on a philosophically lofty topic.[web 2]
People who are initiated into sannyasa in Advaita Vedanta are being taught the four [principal] mahavakyas as four mantras, "to attain this highest of states in which the individual self dissolves inseparably in Brahman".
 Who is this self (ātman)? - that is how we venerate.  Which of these is the self? Is it that by which one sees? Or hears? Smells [etc...] But these are various designations of cognition.  It is brahman; it is Indra; it is all the gods. It is [...] earth, wind, space, the waters, and the lights [...] It is everything that has life [...] Knowledge is the eye of all that, and on knowledge it is founded. Knowledge is the eye of the world, and knowledge, the foundation. Brahman is knowing.
Several translations, and word-orders of these translations, are possible:
Related terms are jñāna, prajñā and prajñam, "pure consciousness". Although the common translation of jñānam is "consciousness", the term has a broader meaning of "knowing"; "becoming acquainted with",[web 8] "knowledge about anything",[web 8] "awareness",[web 8] "higher knowledge".[web 8]
Most interpretations state: "Prajñānam (noun) is Brahman (adjective)". Some translations give a reverse order, stating "Brahman is Prajñānam",[web 1] specifically "Brahman (noun) is Prajñānam (adjective)": "The Ultimate Reality is wisdom (or consciousness)".[web 1] Sahu explains:
Prajnanam iti Brahman - wisdom is the soul/spirit. Prajnanam refers to the intuitive truth which can be verified/tested by reason. It is a higher function of the intellect that ascertains the Sat or Truth/Existent in the Sat-Chit-Ananda or truth/existent-consciousness-bliss, i.e. the Brahman/Atman/Self/person [...] A truly wise person [...] is known as Prajna - who has attained Brahmanhood itself; thus, testifying to the Vedic Maha Vakya (great saying or words of wisdom): Prajnanam iti Brahman.
The knowledge of Brahman [...] is not intuition of Brahman but itself is Brahman.
 OM - this whole world is that syllable! Here is a further explanation of it. The past, the present and the future - all that is simply OM; and whatever else that is beyond the three times, that also is simply OM -  for this brahman is the Whole. Brahman is this self (ātman); that [brahman] is this self (ātman) consisting of four quarters.
While translations tend to separate the sentence in separate parts, Olivelle's translation uses various words in adjunct sets of meaning:
[6.2.1] In the beginning, son,, this world was simply what is existent - one only, without a second. [6.2.3] And it thought to itself: "let me become many. Let me propagate myself." [6.8.3] It cannot be without a root [6.8.4] [l]ook to the existent as the root. The existent, my son, is the root of all these creatures - the existent is their restingplace, the existent is their foundation The finest essence here - that consitutes the self of this whole world; that is the truth; that is the self (ātman). And that's how you are, Śvetaketu.
[1.4.1] In the beginning this world was just a single body (ātman) shaped like a man. He looked around and saw nothing but himself. The first thing he said was, 'Here I am!' and from that the name 'I' came into being. [1.4.9] Now, the question is raised; 'Since people think that they will become the Whole by knowing brahman, what did brahman know that enabled it to become the Whole? [1.4.10] In the beginning this world was only brahman, and it knew only itself (ātman), thinking: 'I am brahman.' As a result, it became the Whole [...] If a man knows 'I am brahman in this way, he becomes the whole world. Not even the gods are able to prevent it, for he becomes their very self (ātman).[note 4]
Ahaṁ Brahmāsmi then means "I am the Absolute" or "My identity is cosmic," but can also be translated as "you are part of god just like any other element."
In his comment on this passage Sankara explains that here Brahman is not the conditioned Brahman (saguna); that a transitory entity cannot be eternal; that knowledge about Brahman, the infinite all-pervading entity, has been enjoined; that knowledge of non-duality alone dispels ignorance; and that the meditation based on resemblance is only an idea. He also tells us that the expression Aham Brahmaasmi is the explanation of the mantra
That ('Brahman') is infinite, and this ('universe') is infinite; the infinite proceeds from the infinite. (Then) taking the infinitude of the infinite ('universe'), it remains as the infinite ('Brahman') alone. - (Brihadaranyaka Upanishad V.i.1)[note 5]
He explains that non-duality and plurality are contradictory only when applied to the Self, which is eternal and without parts, but not to the effects, which have parts. The aham in this memorable expression is not closed in itself as a pure mental abstraction but it is radical openness. Between Brahman and aham-brahma lies the entire temporal universe experienced by the ignorant as a separate entity (duality).
Vaishnavas, when they talk about Brahman, usually refer to impersonal Brahman, brahmajyoti (rays of Brahman). Brahman according to them means God - Narayana, Rama or Krishna. Thus, the meaning of "aham brahma asmi" according to their philosophy is that "I am a drop of Ocean of Consciousness.", or "I am soul, part of cosmic spirit, Parabrahma". Here, the term Parabrahma is introduced to avoid confusion. If Brahman can mean soul (though, Parabrahma is also the soul, but Supreme one - Paramatma), then Parabrahma should refer to God, Lord Vishnu.