More concrete: If we take a human brain apart, we end up with neurons and glia cells, (and a bunch of supporting cast). These all consist of phospholipids, proteins, and nucleic acids (and some more supporting cast). These then all consist of atoms, which consist of quantum particles. No matter how much we look around, that's all that we find in the brain.
This is a reductive approach. If you do reduction, it's like you're differentiating a formula where you keep losing terms on the right hand side. At every reduction step something similar happens: you are losing information about how your parts are organized.
When you integrate, the terms you differentiated out before will show up again. What sort of magic is this, you ask? There is no magic, those terms were there before. Now that you're doing the opposite (complementary) operation, they're coming back.
So by reducing the brain down, we didn't find any singular component that provides consciousness or thought or any such thing. Having eliminated those, whatever remains must be the truth. But what remains?
The only thing that we've missed is the information that we threw out when we were doing reduction. Apparently consciousness and thought and image recognition and pain and feelings must arise from the organization of the components. This is what is called the "emergent properties".
* You can try the same operation with reducing a game computer down to single transistors. You'll find that this is insufficient to explain how Mario works. You need to look at how the transistors are organized into gates, and how the gates are organized to form memory and instructions, and then how those in turn can be used to execute programs. [2]
* Another similar experiment might be to try to find out what makes a watch tick. You can certainly take it apart, but at the end of the day you are left with a pile of parts that definitely don't tick anymore. You have to put them back together in a very specific way to ultimately recover the emergent property: ticking.
[1] https://news.ycombinator.com/item?id=34619834
[2] Inspired by https://journals.plos.org/ploscompbiol/article?id=10.1371/jo...