The nature of neural networks is perhaps better understood by more people nowadays than used to the be the case. Forms of neural network are used for a range of computational purposes, where they have proved useful as a way to economically discover solutions to difficult problems in pattern recognition, optimization, and other fields. How a particular solution works isn’t always clear, especially when using larger networks, but if it can be proven to work well then why worry?
We ourselves are neural networks: the complex adaptive phenomena that we choose to call the self arises from comparatively simple exchanges between many, many neurons. The machine is the connections and the state of its neurons, constantly altering itself in response to circumstances and its own operation.