Neural network is a fairly broad term that covers a number of related methods but, in our case, we will focus on a feedforward network that trains with backpropagation. I'm not going to waste our time discussing how the machine learning methodology is similar or dissimilar to how a biological brain works. We only need to start with a working definition of what a neural network is.
To know more about artificial neural networks, I think the Wikipedia entry is a good start: https://en.wikipedia.org/wiki/Artificial_neural_network.
To summarize, in machine learning and cognitive science, artificial neural networks (ANNs) are a family of statistical learning models inspired by biological neural networks (the central nervous systems of animals, the brain) and are used to estimate or approximate functions that can depend on a large number of inputs...