A common criticism for the philosophy of Advaita or Non-dualism is that it is not practical. Many a seeker feels that this teaching cannot reconcile with what is the perceived reality of the world. This is because, to the seeker, what is called the Illusion or the world and its activities goes on despite the assertions of the Guru that it all nothing but an illusion. When carefully probed it becomes clear that the problem is not in Advaita. On the contrary, it is obvious that the very problem lies in the seeker having not found out his True Nature. On realizing one's True Nature, the Truth remains and the Illusion remains only as an illusion. The Illusion does not disappear for the so called "me' since the "me' and the illusion are one and the same. The "me" is part of the illusion. One cannot be a part of the illusion and see the illusion for what it is. Just like a person who is sleeping cannot tell you that he is sleeping well. The seeker wants to maintain his identity while investigating into the nature of the Truth. How can the seeker realize the Truth with this condition of maintaining a separate identity? Only when the feeling "me' as being a separate entity with independence subsides does the Truth become apparent and obvious immediately. Yet, there is actually no one to claim observance or realization of the Truth. Truth is not an object to be realized. Truth is itself the grounds or the substratum upon which all of manifestation arises. Because it is difficult to put Truth into words for communication, one has to rely on commonly used words in language to point to the Truth. Yet the word is not the thing and this must be borne in mind when investigating into the nature of Truth. The question of reconciling Truth with the Illusion can only arise for a seeker who has not fully Realized the Truth. For upon Realization, there is no one to put forward any questions. The seeker has merged in the Truth. Only Truth remains.
May be this analogy will help in understanding your True Nature. A wave is nothing but the water of the ocean with a form. In reality, the wave is nothing but water. The ocean is nothing but water. When a wave has merged into the ocean, it is nothing but the ocean itself. Can a wave that has merged in the water of the ocean ever make claims to being a wave? Can the wave that has merged in the ocean and can never be apart from the ocean, have any identity now? In the same way, a wave which Realizes its own True Nature as being only the ocean (or the water of the ocean), can calmly relax being a wave without worrying about its future and its own impending destruction as a form. The wave on Knowing its own True Self does not get destroyed as a form immediately but continues on its journey as a wave. Such a Realized Wave can tell other non-realized waves that they are in reality just the water of the ocean. Such a Realized Wave can tell other non-realized waves that they did not choose to be born as a wave and they have no control on when the form as a wave will subside. The wave form has appeared on the surface of the ocean and will spontaneously merge back into the ocean when its time is up. The non-realized waves, assuming themselves to be forms with different shapes and sizes, have overlooked the fact that they are after all nothing but the water of the ocean in reality. The non-realized waves have falsely taken the form to be the reality and ignored their true nature which is water. Such a Realized Wave can tell other non-realized waves not to worry about themselves or their future of possibly being relentlessly thrown against a rock or destroyed otherwise against their will. Such a Realized Wave can tell other non-realized waves that they are not apart from the ocean in any way and have never ever been apart from the ocean. In fact, the ocean is the substratum of their existence as a wave. In fact, the waves all arise and subside into the ocean. The ocean remains as it always has been, unchanged as a body of water.
Your True Nature or your True Self is like the water, the water at the bottom of the ocean, Still and Peaceful and undisturbed by the world of activities and turmoil which is apparent on the surface. Be Your Self.