What is the difference between Atman and Brahman?
This is one of the most fundamental questions in Advaita Vedanta philosophy.
Brahman refers to the ultimate, infinite, undivided Reality -- the ground of all existence. It is pure Being-Consciousness-Bliss (Sat-Chit-Ananda). Brahman is without form, without qualities, without parts. It is not a God "up there" -- it is the very substratum of reality, closer to you than your own breath.
Atman refers to the individual self -- the innermost witness-consciousness within the individual, the pure awareness that observes all thoughts, feelings, and experiences.
The central teaching of Advaita Vedanta, as articulated by Adi Shankaracharya, is expressed in the Mahavakya from the Chandogya Upanishad: "Tat Tvam Asi" -- "That (Brahman) thou (Atman) art." The individual self and the universal Self are not ultimately two separate things -- they are one and the same Reality.
The appearance of separation is due to avidya (ignorance) and maya (the power of creative illusion). When knowledge (jnana) removes this ignorance through spiritual inquiry and the grace of a teacher, what remains is the recognition that Atman is Brahman.
In the traditions of Dvaita (Madhvacharya) and Vishishtadvaita (Ramanujacharya), the relationship between Atman and Brahman is understood differently -- as a real distinction between finite souls and the infinite divine. These are serious philosophical positions held by great thinkers, and the debate between them represents one of the most sophisticated conversations in the history of human philosophy.