The concept of Ayam Atma Brahman is explained as Atman and Brahman being the same. A Mahavakya in Hinduism, this saying portrays the idea that the individual self is one and the same with the absolute.
The concept Ayam Atma Brahman is explained with the wave and ocean. The waves and ocean is not considered as separated entity, similarly Atma and Brahman is the same. The aspirant can clearly understand this Mahavakya by taking up the example of the ocean and watching the vastness of the ocean. If a big wave starts to come ashore, and one concentrates on one wave, he can intently notice that the wave get absorbs in the crashing of the surf, and he can feel the salt spray. In that moment, the person is only aware of the vastness of this one wave. The ocean itself is forgotten during that time. The only idea then prevails is that the ocean and the wave is the same and the one.
Atman refers to that pure, perfect, eternal spark of consciousness that is the deepest, central core of human being. While, Brahman refers to the oneness of the real and unreal universe. It is like saying that atman is a wave, and brahman is the ocean. The insight of Ayam atma brahma is that the wave and the ocean are one and the same.
Ayam atma brahma is a statement, specially framed that denotes the observer to be a separate observer of both Atman and Brahman. It is like standing at the beach, looking out at both the wave and the ocean and declaring that the wave of the ocean is one. The person trying to understand this Mahavakya is observing from a witnessing stance who is not related to either Atma or Brahma. This happens to be a perspective contrast with Aham brahmasmi (I am Brahman), which declares that "I am!" an inner experience, rather than from an observing standpoint.
Each of the Mahavakyas gives a different perspective of the same underlying Reality. This Mahavakya is seen as mirror reflections of the same Absolute Reality. The incorporated flash of insight confronts the true meaning of the word brahman. It is like gaining different points of view from different viewing points. Together, they converge in a complete understanding.
To attain the true meaning of Ayam atma brahma, the aspirant has to sit quietly and reflect on the inner core of his real being, such as by placing his attention in the space between the breasts at the exact heart centre. He should not visualize anything, but allow his awareness to touch the feeling aspect of the centre of his existence. Or, if he prefers to visualize internally, he can imagine a tiny spark of light that represents the eternal essence your own self, the atman. On holding this attention for a few seconds or minutes, he can realise the meaning of Ayam atma brahma.
Then, slowly he should shift his attention in such a way that he is imagining the breadth of the entire real and unreal universe, the gross, subtle, and causal realms. The person will eventually realise the oneness that pervades all and is the absolute. This act should be done in a way that you are aware of the spirit in which all exists, like being aware of the gold or the clay. Steadily, the aspirant should allow his attention to capture both the awareness of the spark that is atman and the universal essence that is brahman. Atman also being within that oneness of Brahman will be understood soon. This evolution of thought will bring insight and peace. The person may want to internally the words of the Mahavakya, "Ayam atma brahma; atman and brahman are the same."
The understanding of Ayam atma brahma is a beautiful practice and one should do the same thing in relation to other people. He should think of the people who are closest, including family, friends, and co-workers. He should allow himself to notice the surface levels of their actions and speech, their physical features, and their personalities. One should be aware of the subtle aspects of their composition, and of the spark of the perpetual that is the centre of their consciousness. Be aware of how that spark, atman, is one with the oneness, Brahman.
One should notice the different ideas and feelings between the Mahavakyas. The insight from Tat tvam asi (That is who you are) is experienced is a very different way from Ayam atma brahma (This individual Self is one with the absolute). The two of the Mahavakyas are different internally, however they work together, describing the same primary truth about who the human beings are. By experiencing the separate vantage points, the whole meaning of Ayam atma brahma is more completely experienced.