The passage
It closes chapter 2 of the Zhuangzi, the chapter usually rendered as "On the Equality of Things". Zhuang Zhou dreams he's a butterfly, flitting about, entirely convinced and entirely happy, with no awareness of being Zhuang Zhou. He wakes, unmistakably himself, and can't tell whether he's a man who dreamt he was a butterfly or a butterfly now dreaming it's a man.
Then comes the line everyone drops: "Between Zhou and the butterfly there must be some distinction. This is called the transformation of things."
That last sentence is the whole point, and it's the one that gets cut from the poster.
What it's usually mistaken for
The popular reading turns it into an early version of the simulation argument: how do you know you're awake, how do you know any of this is real, cue the film clip. Descartes asked that question and meant it. Zhuangzi isn't.
He never suggests the dream was unreal or that waking life is suspect. Both states were completely convincing from the inside. He doesn't try to resolve which is which, and he isn't bothered that he can't. A skeptic who found the question genuinely alarming would keep pushing. Zhuangzi shrugs and names what happened.
What it's actually arguing
Chapter 2 spends its length dismantling the idea that our categories carve reality at its joints. Right and wrong, big and small, useful and useless, self and other: Zhuangzi keeps showing that these depend on where you're standing. A beam can batter down a city wall and can't plug a small hole. Neither fact makes it good or bad.
The butterfly lands that argument on identity. "Zhuang Zhou" felt total while it lasted, and so did "butterfly", and the boundary between them turned out to be permeable in a way neither state could see from inside. There is a distinction. What there isn't is a fixed vantage point from which to rank them.
"The transformation of things" is the Taoist name for that permeability. Things become other things. You have been a child and will be old, and each state was completely convincing while you were in it. The dream is a compressed demonstration rather than a riddle awaiting an answer.
Why it's the most Taoist thing in the book
Notice the emotional register. Zhuangzi's response to radical uncertainty about his own identity is delight. The butterfly was happy. He reports the confusion the way you'd report good weather.
That's the difference between Taoist skepticism and the anxious Western kind. The point of loosening your categories isn't to arrive at a better one. It's to stop gripping. Our guide to letting go follows that thread, and the wider Zhuangzi guide covers the stories around it.
Where to read it
Any translation of the Inner Chapters gives you the passage in under a page. Burton Watson's rendering is the one most people quote. If you're working through Taoism at a slower pace, 365 Days of Tao takes the Tao Te Ching one verse a day across a year, and the daily Tao email is the free version of the same thing.
Common questions
What is the meaning of Zhuangzi's butterfly dream?
That the boundaries between states of being are more permeable than they feel from inside. Zhuangzi calls it 'the transformation of things'. He isn't asking whether reality is real; he's showing that no state gives you a fixed vantage point over the others.
Is the butterfly dream about simulation theory?
No, though it gets used that way. Zhuangzi never doubts that either state was real, and he isn't troubled by being unable to rank them. Descartes asked that question anxiously; Zhuangzi asks it cheerfully and moves on.
Where is the butterfly dream in the Zhuangzi?
At the very end of chapter 2, one of the seven Inner Chapters generally accepted as Zhuang Zhou's own writing.
What does 'the transformation of things' mean?
The Taoist observation that things continually become other things, and that the borders we draw between them are conventions rather than facts about the world.
Did Zhuangzi believe life was a dream?
He doesn't say so. He points out that he can't establish which state has priority, and finds that funny rather than frightening.