In Advaita
Tat tvam asi is the Mahāvākya (Grand Pronouncement) from Chandogya Upanishad. The Advaita school of Shankara assigns a fundamental importance to this Mahāvākya and three others of the same kind from three other Upanishads. This is actually a statement meted out by Sage Aruni to Shvetaketu, his son. It says literally 'That thou are'. In other words that Brahman which is the common Reality behind everything in the cosmos is the same as the essential Divinity, namely the Atman, within you. It is this identity which is the grand finale of Upanishadic teaching, according to Advaita. The realisation of this arises only by an intuitive experience and is totally different from any objective experience. It cannot be inferred from some other bit of knowledge. To comprehend the meaning an analysis of the three words in the pronouncement is needed.
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