It is among the four statements the Advaita tradition designates mahavakyas, great sayings, and it may be the most consequential three words in Indian philosophy. It is also translated in two incompatible ways.
The setting is the sixth chapter of the Chandogya Upanishad. Uddalaka Aruni is instructing his son Shvetaketu, who has returned from twelve years of Vedic study rather pleased with himself. The father takes him through a series of demonstrations, clay and clay pots, salt dissolved in water, a banyan seed, each ending with the refrain, and the refrain is repeated nine times.
The traditional reading, and Shankara's, takes tat as the ultimate reality and tvam as the individual, and reads an identity: that you are. On this reading it is the compressed statement of non-duality, and the whole of Advaita Vedanta is an unfolding of it. Ramanuja read the same words within a qualified non-dualism, and Madhva performed a word division that produces the opposite sense, that you are not, which is grammatically possible in Sanskrit and is not a joke.
A separate modern proposal, from Joel Brereton, reads tat not as an ultimate but as referring back to the specific example just given, so the refrain would mean something closer to "that is how you are", the point being pedagogic rather than metaphysical. That reading is argued from the structure of the chapter and is taken seriously by Sanskritists without having displaced the traditional one.
Three words, four readings, and the schools of Vedanta divide along them.