Everybody dreams. Some remember, most don't. Some remember some dreams vividly. Yesterday, I had such a dream. The short part of it was that I was dancing with two friends. I don't know them in real life, so lets call them Ram and Shyam. (If I had known these people also, it wouldn't make an iota of difference to this topic). In real life, I don't really go to parties, let alone dancing! Dreams originate from impressions left by experiences in waking state, says Bhagavadpada Shankaracharya. So this dream dancing must have surely come from some experience of mine in this life or past, or an assemblage of various experiences drawn from various lives, movies, etc.
We are used to recalling dreams w.r.t. dream objects, people and situations. However, if we look at what the dream really is, it has no ground to stand on! What is the reality of the dreamer? He was me, since I was conscious of him during the dream and I can even relate to him now, if I think of the dream. The dreamer's body, mind and senses were all created by me, using my own knowledge of his body, mind, and senses. No one taught the dreamer that ridiculous party dance, but that was only my knowledge of dance. Now, we go a step further to see that not only all these factors relating to the dreamer were my knowledge, but the same factors about Ram and Shyam were my knowledge alone. What was to happen in the party, how Ram and Shyam thought, spoke, acted, were all defined by me. Of course, the dreamer thought others to have their own individualities, because the dreamer didn't know what Ram and Shyam thought. In fact, Ram and Shyam, the entire party, with all the people and objects, the air they breathed, the food they ate, etc, were all nothing but my knowledge! This knowledge resides in my consciousness and therefore they were all truly me!! The truth of the entire dream world is the conscious being who is dreaming; that conscious being is me. Remember, the dreamer thinks he is awake! Herewith ends the example.
Similarly, this waking world is a dream. It includes all of us sentient beings like people, animals, birds, trees, etc and insentient objects like mountains, rivers, etc. The world was created out of nothing but pure knowledge of the world. That knowledge exists in a conscious being. That conscious being is Ishvara. I am the dreamer of Ishvara's dream creation and I think I am awake! Since the dreamer is the same as the waker, in this waking dream of Ishvara, Ishvara is the truth of me. Ergo, I am Ishvara. अहं ब्रह्मास्मि।