They are the Mahavakyas, the Great sayings, the four Vedic aphorisms, four Sanskrit sentences which sum up the doctrine of Advaita Vedanta, Vedanta non-dualist, which believes that reality is one and only one, that reality is Brahman with whom also the individual soul identifies.
Tat tvam asi means You are that (Chandogya Upanishad VI, 8, 7)
Aham Brahmasmi means I am Brahman (Brhadaranyaka Upanishad I, 4, 10)
Ayam atma brahman, This Self is Brahman (Mandukya Upanishad II)
Prajnanam Brahma ie Brahman is pure Consciousness (Aitareya Upanishad V, 4)
While the first three sayings express the concept of identity between the individual spirit (Atman) and the Universal Spirit (Brahman), the forth one indicates the nature of Brahman as pure consciousness, devoid of purpose, modification, and duality.
The knowledge of this non-duality, this identity is the means to achieve moksha, or liberation from samsara, the cycle of rebirths.
The Mahavakyas are used as mantras too.