The best definition of a neural network is provided by an inventor, Dr. Robert Hecht-Nielsen, one of the first neurocomputer scientists, in Neural Network Primer: Part I by Maureen Caudill, AI Expert, Feb. 1989:
...a computing system made up of a number of simple, highly interconnected processing elements, which process information by their dynamic state response to external inputs.
The fundamental building blocks of neural networks are neurons, and they are organized in different layers. The tiered architecture has the neurons in each layer connected to neurons in the next layer. A neural network has, at a minimum, three layers. The input layer is connected to one or more hidden layers, where the connection is established through a system of weighted links. The last hidden layer is connected to the output layer which produces the results of a task...