In plain words
The pleasure of sense objects, whether it is found in this world or in another, is worthless. To gain the strength to recognise that it is merely transient, like the scenes of a dream: that alone is Virāga toward the enjoyment of fruits. The mansions and terraced houses of a dream are gone the very moment you open your eyes, are they not! The scenes you see with open eyes in the waking state appear as Asatya in a dream; the scenes of a dream are Asatya in the waking state. In what bodies you dwelt before this birth, there is no telling of them; and who can tell what kind of body will come to you after you pass away?
So you must understand only this: each state is real for its own time. You must understand that the experiences in the world, conjured up out of what is seen, are merely of the nature of mithyā, or else of the nature of a dream.
You need not go that far. If each of you calls to mind your own daily experience, the fact that the world is mithyā becomes clear. Many people accept the proof of direct perception and hold it in esteem. But Vedānta does not accept the proof of the senses in the least. Today all of you sit in this auditorium, listen to Swami's words and the words of the paṇḍits, and take them in with your hearts: “This is real. It is not Asatya”: this you can believe! A few hours from now, when this meeting is over, you will have your meal, lie down to sleep in this very auditorium, and while you sleep a dream will come to you. Your body is sleeping right here, yet in that dream you experience it as though you were wandering about the city of Calcutta, or Delhi, or Bombay, doing your shopping. It never once occurs to you that the scene you see in the dream state is not real.
Everything you experienced in the auditorium in the waking state is real indeed! Your wandering about Calcutta, Delhi and Bombay in the dream state is just as real! If you inquire how that can be, it becomes clear to you yourself: the one present in both states is you alone. So you alone are Satya. What appeared in the waking state is a Day dream (divā svapnamu), a dream of the daytime. What appeared in the state of sleep is a Night dream (niśā svapnamu), a dream of the night. That is all the difference there is! What is one way in the one state and another way in the other is not Satya. Only what stays the same in both is Satya. Truth is one, not two.
That is why Śaṅkara gave his life to discerning Satya and mithyā, to teaching them, to giving people eternal sayings and bringing them into the Eternal. Keeping this in view, he went on proclaiming, “Brahma satyaṃ, jaganmithya.” The Paramātma is in Satya and in mithyā alike! That itself is the supreme Satya. What is not Satya is mithyā. But nowhere is there any separate thing called mithyā! Darkness means only the absence of light, but it is not some other thing that stands apart. What is, is one alone! A second is sheer delusion.