A neural network is an array of layered nodes, where each node contains some kind of activation function, and each connection represents some weight multiplier. Importantly, once the model is trained, it's stateless, meaning we don't need to store any extra data to use it - just inputs and outputs.
If we could take some sort of material, like a glass, and modify it so that if you shone a light through one end, the light would bounce in such a way as to emulate these functions and weights, you could create an extremely cheap, compact, fast, and power efficient neural network. In theory, at least.