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A single neuron can only ask one question. That's not enough for real problems, which depend on combinations of things like the shape of an ear and the proportions of a face. No single rule can capture that.
So you stack neurons into layers. That gives the network more power, but it also creates a harder question: when the answer is wrong, which weights caused the mistake?
Don't worry if backpropagation and gradient descent felt like a lot. You do not need to remember the names.
Here is the idea worth keeping: when a network gets something wrong, there is a way to trace the mistake backward, give each weight its share of responsibility, and nudge the whole system toward a better answer.
The machine is not being handed the solution. It is correcting its way there, one mistake at a time.