While training the neural network we try to find the mathematical formula that best maps the input to the output. We do this by tweaking each neuron (each neuron is a parameter in our formula). The interesting part is that each layer of the neural network will start acting like a feature extracting step - just like our signal processing step - but highly tuned for your specific data. For example, in the first layer, it'll learn what features are correlated, in the second it derives new features, and in the final layer, it learns how to distinguish between classes of motions.