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Nobody tells the hidden layers what to look for. No engineer decides what matters. No expert writes down the intermediate steps.
The hidden layers figure it out on their own. The only feedback they get is whether the final output was right or wrong, and the correction that flows back from that.
What emerges from that process is often readable. Take a network trained to recognize images. The first hidden layer tends to notice edges: small differences in brightness between neighboring pixels. That's it, nothing more complex.
The second layer takes those edges and combines them into shapes. The third layer combines shapes into parts of objects, like an ear or an eye.
By the final layer, the network is working with something that functions like the concept of "dog" or "face," though it has no idea what those words mean, and no one told it to build those concepts.
Nobody programmed any of that. The network invented those intermediate steps because they turned out to be useful for getting the right answer.
The knowledge isn't written down anywhere. It's discovered. That's the sharp line between this approach and the rule-based systems that came before.