Recently I was watching a lot of vidoes on you tube of famous seers of India and philosophical Gurus talking on the ultimate reality and nature of ultimate reality. Having known the words that are often used in such discussions like Brahaman, Atman, Maya etc. and having a cloudy idea on those makes it a little easier to understand the lectures on such philosophies.
In some of the discussions, the core philosophy is directly thrown at audience and it is often very hard to grasp the hard reality that these philosophers tries to project and throw at their audiences. In other discussions, the concept is brought little slowly like a complex looking mathematical formula is derived from some basic concept or understanding step by step.
One such step by step method of realising the core tenet of Advaita philosophy is through our experience of the world and objectifying our experience. It very simplistically and innocently says that whatever is experienced and what is being experienced cannot be the same. This simple and basic philosophical concept looks very logical as the observer and the observed are always different in our day to reality. But this small principle is the base on which the first leg of Advaita philosophy stands.
It is very easy to say from our experience of day to day reality of the world that anything outside the body is separate entities from what we would say ourselves. So from our existing concept of reality, the world except of our body is the object of our experience.
However, Advaita philosophy digs it deeper to say that as the sensory organs 'sees' the world outside, it is the mind that sees the body. However, the body and the mind are experienced by ourselves and therefore by the logic of basic phylosophy, the experiencer is not the body and mind. Here the advaita Philosophy gives the concept of Brahman the experiencer of the body-mind complex which is said to be 'the reality' and experiences of what we call 'reality'.
Brahman, said to be 'the reality' in Advaita philosophy is the consciousness that experiences everything that we call reality. Now the big question arises - then what are the material world we see and objects of experience to Brahman. Advaita philosophy says there since there is no other than the Brahman-the consciousness the reality that we see are not separate from Brahman itself and are its own projection that originates and exists in Brahman.
Since the philosophy concludes that there is no other than Brahman, everything that we experience in our reality including us is 'that one reality', Brahman. Therefore the philosophical expression - Aham Brahmasmi, meaning - 'I am Brahman'. Advaita btw means non-dual or without a second which very simplistically carries the very inner philosophy that it propagates.